Thomas Wieder

J. Zendehroud, T. Wieder, K. Thoma, H. Gärtner.
Tiefenauflösende röntgenographische Dehnungsmessungen an TiN-Schichten in Seemann-Bohlin-Geometrie;
Härterei-Technische Mitteilungen 48 (1993), 41 - 49.

W. Siejkowski, A. Calderero-Lopez, T. Wieder and H. Gärtner:
X-Ray Analysis of Oxidized and Sulfidized Thin Nickel Films;
Metalurgia I Odlewnictwo (Polen) 17, (1991), 427 - 434.

H. Gärtner, K. Thoma, H. Volkmann, T. Wieder, A. Schmitt:
High-energy implantation of Kr+ into Ti;
Nuclear Tracks and Radiation Measurement (UK), 19 (1991), 885 - 890.

T. Wieder:
Berechnung des (420)-Reflexprofiles einer gamma'-Fe_3N_(1-x)-Schicht mit Säulenstruktur und Dehnungsrelaxation;
Materialwissenschaft und Werkstoffkunde 22 (1991), 23 - 30.

T. Wieder, W. Herr und H. Gärtner:
Berechnung von Röntgenreflexen für polykristallines Titan unter dem Einfluß von Stickstoffgradienten und Eigenspannungen;
Materialwissenschaft und Werkstoffkunde 20 (1989), 271 - 277.

T. Wieder, K. Thoma and H. Gärtner:
New Scattering Formula for the Analysis of X-ray Line Broadening by Composition Profiles;
Applied Physics A 46 (1988), 165-167.

K. Thoma, R. Färber, T. Wieder and H. Gärtner:
Structure and Fatigue Properties of Ion-plated Nickel Films on Steel;
Materials Science and Engineering 90 (1987), 327 - 332.

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Buchbeitrag:

U. Schubert, T. Wieder:
Ein Strukturmodell des amorphen SiO;
Jutzi, Peter / Schubert, Ulrich (eds.)
Silicon Chemistry
From the Atom to Extended Systems
Wiley-VCH, Weinheim, 1. Auflage - Juli 2003
ISBN 3-527-30647-1.

Hochschulschriften:

T. Wieder:
Realstrukturaufklärung polykristalliner dünner Schichten mittels Röntgenbeugung;
Habilitationsschrift, FB Materialwissenschaft, TH Darmstadt, 1997.
Erschienen als elektronische Publikation bei Kassel University Press, ISBN 3-933146-01-1.
Kassel University Press

T. Wieder:
Eine neue Streuformel für die tiefenauflösende Röntgenstrahldiffraktometrie nach der kinematischen Theorie;
Inaugural-Dissertation, FB Physik, Gesamthochschule Kassel, 1988.

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Konferenzberichte, Posterzusammenfassungen:

T. Wieder:
The Debye scattering formula in n dimensions;
26 European Crystallographic Meeting, Darmstadt, 2010,
Acta Crystallographica A66 (2010), 217.

A. Hohl, T. Wieder, H. Fuess:
Ramanspektroskopie an Siliciummonoxid zur Untersuchung von Kristallitgrößen und Dynamik;
XXV. Tagung des Arbeitskreises nichtkristalline und partiellkristalline Strukturen,
AK4 der Deutschen Gesellschaft für Kristallographie (DGK), Wolfersdorf bei Jena, 2004.

A. Hohl, T. Wieder, H. Fuess:
Ramanspektroskopische Untersuchung der Siliziumkristallisation in Siliziummonoxid;
XXIV. Tagung des Arbeitskreises nichtkristalline und partiellkristalline Strukturen,
AK4 der Deutschen Gesellschaft für Kristallographie (DGK), Wolfersdorf bei Jena, 2003.

A. Hohl, T. Wieder, H. Fuess:
A Structural Model For Silicon Monoxide;
Conference on Non-Crystalline Inorganic Materials, Concim 2003, Bonn, 2003.

A. Hohl, T. Wieder, V. Joco, H. Fuess:
On the Structure of Amorphous Silicon Monoxide;
ILL Konferenz, Grenoble, 2002.

A. Hohl, T. Wieder, H. Fuess:
Disproportionierung in SiO;
XXIII. Tagung des Arbeitskreises nichtkristalline und partiellkristalline Strukturen,
AK4 der Deutschen Gesellschaft für Kristallographie (DGK), Jena, 2002.

N. Bickulova, S. Danilkin, H. Fuess, V. Semenov, A. Skomorokhov, T. Wieder, E. Yadrowski, Z. Yagofarova:
Lattice dynamics and phys transititions in superionic conductor Cu2-δSe;
Proceedings of the Second German-Russian User Meeting “Condensed Matter Physics with Neutrons at IBR2”,
Frank Laboratory of Neutron Physics, Dubna, Russia, 2001.

A. Hohl, T. Wieder, H. Fuess:
Strukturaufklärung bei SiO;
XXII. Tagung des Arbeitskreises nichtkristalline und partiellkristalline Strukturen,
AK4 der Deutschen Gesellschaft für Kristallographie (DGK), Wolfersdorf bei Jena, 2001.

M. Hölzel, S.A. Danilkin, A. Hoser, T. Wieder, H. Fuess:
Phonon dispersion austenitic steels;
Deutsche Neutronenstreutagung 2001, 19-21 Februar 2001, Jülich and Aachen, Abstracts, p. 14.

J. Sigmund, M. Saglam, A.Vogt, H.L. Hartnagel, V. Buschmann, T. Wieder, H. Fuess:

Microstructure analysis of Ohmic contacts on MBE grown n-GaSb layers and investigation of submicron contacts;
MBE-XI: International Conference on Molecular Beam Epitaxy, Beijing, China, 2000, Abstracts, S. 275.

A. Hohl, T. Wieder, H. Fuess:
Eine Studie zur Strukturaufklärung des Siliziummonoxids (SiO);
9. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Bayreuth, 2001,
Zeitschrift für Kristallographie, Supplement Issue 18 (2001), S. 66, ISBN 3-486-64267-7.

A. Njah, T. Wieder, H. Fuess: Grazing excidence diffraction versus grazing incidence diffraction for strain/stress evaluation in thin films;
European Crystallographic Meeting ECM 19, Nancy 2000,
Acta Crystallographia A56 (Supplement, 2000), S. 136.

Ch. Deneke, P. van Aken, T. Wieder:
Elektronen-Energieverlust-Spektroskopie an SiO und a-SiO2;
XXI. Tagung des Arbeitskreises nichtkristalline und partiellkristalline Strukturen,
AK4 der Deutschen Gesellschaft für Kristallographie (DGK), Wolfersdorf bei Jena, 2000.

Jürgen Schreiber, Achim Neubrand, Thomas Wieder, Meinhard Stalder, Nail Shamsutdinov:
Distribution of Macro- and microstress in Cu/W FGM;
Functionally Graded Materials 2000: Proceedings of the 6th International Symposium on Functionally Graded Materials;
Estes Park, Colorado, USA, September 10-14, 2000,
Ceramics Transactions, Volume 114, Wiley-Blackwell (2001), ISBN: 1-57498-110-2.

A. Njah, T. Wieder, H. Fuess:
Streifender Strahlausfall versus streifendem Strahleinfall für Spannungsermittlung an dünnen Schichten;
8. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Aachen, 2000,
Zeitschrift für Kristallographie, Supplement Issue No. 17 (2000), S. 203, ISBN 3-486-64264-2.

H. Fueß, M. Ghafari, A. Hohl, B. Stahl, T. Wieder, M. Winterer:
Nahordnung in Fe100-xScx aus EXAFS-Spektren;
8. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Aachen, 2000,
Zeitschrift für Kristallographie, Supplement Issue No. 17 (2000), S. 104, ISBN 3-486-64264-2.

T. Wieder, T. Pirling:
Eigenspannungen in einem W/Cu-Durchdringungskompositen;
7. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Leipzig, 1999,
Zeitschrift für Kristallographie, Supplement Issue No. 16 (1999), S. 137, ISBN 3-486-64264-2.

D. Zheng, T. Wieder, G. Miehe:
Eine Rietveld-Verfeinerung des amorphen SiO2;
7. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Leipzig, 1999,
Zeitschrift für Kristallographie, Supplement Issue No. 16 (1999), S. 131, ISBN 3-486-64264-2.

T. Wieder:
Rietveld-Analyse amorpher Strukturen;
XX. Tagung des Arbeitskreises nichtkristalline und partiellkristalline Strukturen,
AK4 der Deutschen Gesellschaft für Kristallographie (DGK), Wolfersdorf bei Jena, 1999.

M. Baeva, A. Beskrovni, S. Danilkin, H. Fuess, E. Jadrowski, T. Wieder:
X-Ray and Neutron Study of Crystal Structure and Lattice Dynamics of Fe-Cr-Mn-
and Fe-Cr-Ni-Nitrogen Steels with Different Mn and Cr Content;
Deutsche Neutronenstreutagung, 25-27 May, 1999, Potsdam, Germany, Abstracts, p. 174.

D. Zheng, T. Wieder, G. Miehe, H. Fuess:
Rietveld refinement of amorphous SiO2;
Euroseminar "Integrated Analysis of Defekt Structures",
Freiberg, Germany, 1998.

T. Wieder:
Anwendung der generalisierten Debyeschen Streuformel
auf die Strukturbestimmung von amorphem SiO2;
6. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Karlsruhe, 1998,
Zeitschrift für Kristallographie, Supplement (1998), ISBN 3-486-64262-6.

S. Danilkin, H. Fuess, T. Wieder, H. Wipf , E. Yadrowski:
Interstitial Atom Effect on the Structure and Lattice Dynamics of Nb and Fe-based Alloys;
Proceedings of the German-Russian User Meeting, Condensed Matter Physics with Neutrons at IBR-2,
Frank Laboratory of Neutron Physics, Dubna, Russia, April 2-4, 1998, p. 111 - 116.

S. Danilkin, H. Fuess, E. Jadrowski, T. Wieder, H. Wipf:
X-Ray and Neutron Scattering Study of the Niobium-Oxygen Solid Solutions;
The Seventeenth International Conference on Applied Crystallography, August 31 – September 4, 1997, Wilsa-Jawornik, Poland.

S. Danilkin, H. Fuess, E. Jadrowski, T. Wieder, H. Wipf:
Crystal Structure and Lattice Dynamics of Niobium-Oxygen Solid Solutions;
Proceedings of the National Conference for Application of the X-ray, Synchrotron Radiation, Neutrons and Electrons in the Materials Science,
RSNE’97, Moscow-Dubna 25-29 May 1997, Russia, vol 3, p. 15 - 18.

T. Wieder, H. Fuess:
On the generalized Debye scattering equation;
Konferenzbericht European Powder Diffraction (EPDIC) 5, Parma, 1997,
Materials Science Forum 278-281 (1998), p. 100 - 105,
ISSN 0255-5476 (Trans. Tech. Publications, Schweiz),
Part 1 als Buch: ISBN 0-87849-808-7.
doi: 10.4028/www.scientific.net/MSF.278-281.100

T. Wieder, H. Fuess:
A generalized Debye scattering formula;
5. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Hamburg, 1997;
Zeitschrift für Kristallographie, Supplement No. 12, (1997), S. 208, ISBN 3-486-64256-1.

T. Wieder, H. Fuess:
Gitterkonstantenbestimmung an dünnen Schichten;
4. Jahrestagung der Deutschen Gesellschaft für Kristallographie, Marburg, 1996,
Zeitschrift für Kristallographie, Supplement No. 11, (1996), S. 135, ISBN 3-486-64253-7

T. Wieder, J. Zendehroud:
Thermal Strains In Thin Films And Grazing Incidence X-Ray Diffraction;
European Crystallographic Meeting ECM 15, Dresden, 1994.

B. Dorn, M. Schwörer, T. Wieder, I. Munder:
Mechanical and Analytical Characterization of TiAlCN-films;
VI-th Israel Materials Science Conference, Dead Sea, 1993.

Rosa Santa, Thomas Wieder, Herwig Bangert, Alfred Wagendristel:
Stress and Grain Size Determination in Cu-Pb Sputtered Thin Films;
3rd European Vacuum Conference, EVC-3, Wien, 1991,
Pergamon Press, Oxford, 1992.

H. Gärtner, K. Thoma, H. Volkmann, Th. Wieder, A. Schmitt, D.M. Rück, B.H. Wolf:
High-Energy Implantation of Kr+ into Ti;
15th International Conference on Particle Tracks in Solids, Marburg, 3 - 7 September 1990,
Pergamon Press, Oxford, 1990, ISSN 0191-278x.
International Journal of Radiation Applications and Instrumentation. Part D. Nuclear Tracks and Radiation Measurements 19 (1991), 885 - 890.
doi: 10.1016/1359-0189(91)90334-E

W. Siejkowsi, T. Wieder, and H. Gärtner:
X-Ray Diffraction on oxidized and sulfidized Magnetron-sputtered thin Nickel films;
Powder Diffraction, Satellite Meeting of the XVth Congress of the International Union of Crystallography, Bordeaux, 1990.

Th. Wieder, K. Thoma, H. Gärtner:
Ion Implantation into metals at very high energies;
Proceedings of the Workshop on Experiments and Experimental Facilities at SIS/ESR, Darmstadt, March 30 – April 1, 1987,
GSI Report GSI-87-7, ISSN 0171-4546.

R. Färber, K. Thoma, T. Wieder und H. Gärtner:
Ionenplattierte Nickelschichten auf Stahl;
PVD '86, Internationale Tagung 11./12. März 1986 in Darmstadt, S. 309 - 324.

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Annual Reports:

A. N. Skomorokhov, V. A. Semenov, A. Hohl, T. Wieder:
Experimental report on INS measurements on amorphous SiO performed using the DIN-2PI spectrometer;
Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research (JINR), Dubna, Russia, 2003.

A. Hohl, T. Wieder, H. Fuess, A. Njeh, A. Zimina, S. Eisebitt:
Resonant inelastic X-ray scattering on amorphous silicon monoxide (SiO);
BESSY Jahresbericht 2003, Berlin, 2003.

A. Hohl, T. Wieder, V. Joco, H. Fuess, S. Gottschalk, A. Volland, M. Ghafari, M. Fieber-Erdmann:
EXAFS spectroscopy of amorphous iron-scandium alloys Fe100-xScx;
BESSY Jahresbericht 2002, Berlin, 2002.

A. Hohl, T. Wieder, V. Joco, H. Fuess, M. Fieber-Erdmann, and F. Schäfers:
Si K-edge NEXAFS spectroscopy of amorphous silicon monoxide (SiO);
BESSY Jahresbericht 2002, Berlin, 2002.

T. Wieder, A. Hohl, M. A. Gonzalez:
The Structure of Amorphous Siliconmonoxide SiO;
ILL Annual Report 1999.

S. Danilkin, T. Wieder, H. A. Graff, A. Hoser:
Phonon dispersion in Fe-Cr-Mn(Ni) austenitic steel;
HMI Jahresbericht 1999, Hahn-Meitner-Institut, Berlin, 1999, p. 147 .

A. Hohl, T. Wieder, M. Ghafari, B. Stahl, M. Winterer, M. Tischer:
Short Range Order in Fe(100-x)Sc(x) from EXAFS spectra;
HASYLAB Annual Report 1999,
HASYLAB, Hamburg, 1999.

A. Hohl, T. Wieder, M. Knapp:
Radial Distribution Function of Silicon Monoxide (SiO);
HASYLAB Annual Report 1999,
HASYLAB, Hamburg, 1999.

C. Wahl, T. Wieder, M. Knapp:
Residual stresses in an interpenetrating W/Cu composite;
HASYLAB Annual Report 1998,
HASYLAB, Hamburg, 1998.

D. Zheng, T. Wieder, K. Haberle, M. Knapp:
Rietveld refinement of amorphous SiO2;
HASYLAB Annual Report 1998,
HASYLAB, Hamburg, 1998.

H. Wipf, S. Danilkin, E. Jadrowski. H. Fuess, T. Wieder:
X-ray and neutron scattering study of the Nb-O-solid solutions;
Frank Laboratory of Neutron Physics of the Joint Institute for Nuclear Research (JINR), Dubna, Russia, 1998.

T. Wieder, T. Priling, A. Neubrand, H. Fuess:
Residual Stress Measurement in a Gradient Material;
ILL Annual Report 1997,
ILL, Grenoble, 1997.

W. D. Kaplan and G. Kimmel, T. Wieder, K. Thoma and H. Gärtner:
Ion Implantation of MoNi and La-Ga Alloys;
GSI Scientific Report 1990, Gesellschaft für Schwerionenforschung,
Darmstadt 1991, p. 238, ISSN 0174-0814.

T. Wieder, K. Thoma and H. Gärtner:
Surface strains in polycrystalline metals induced by deep ion implantation;
GSI Scientific Report 1988, Gesellschaft für Schwerionenforschung,
Darmstadt 1989, p. 239, ISSN 0174-0814.

T. Wieder, W. Herr and H. Gärtner:
Calculation of the influence of a nitrogen concentration gradient on
the results of X-ray residual stress measurements;
GSI Scientific Report 1988, Gesellschaft für Schwerionenforschung,
Darmstadt 1989, 238, ISSN 0174-0814.

T. Wieder, K. Thoma and H. Gärtner:
Implantation of Cs ++ into Ti;
GSI Scientific Report 1987, Gesellschaft für Schwerionenforschung,
Darmstadt 1988, p. 266, ISSN 0174-0814.

T. Wieder, K. Thoma and H. Gärtner:
Depth Resolving X-ray Analysis of Ion Implanted Metal Surfaces;
GSI Scientific Report 1987, Gesellschaft für Schwerionenforschung,
Darmstadt 1988, p. 267, ISSN 0174-0814.

T. Wieder, K. Thoma and H. Gärtner:
X-ray analysis of Cs implanted into Ti;
GSI Scientific Report 1986, Gesellschaft für Schwerionenforschung,
Darmstadt 1987, p. 247, ISSN 0174-0814.

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Technische Berichte / Technical Reports:

OEIS

Pointers to some comments or sequences contributed by me to the The On-Line Encyclopedia of Integer Sequences (OEIS).

A000041

a(n) = number of partitions of n (the partition numbers). / Comment

A000070

Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041). / Comment

A000079

Powers of 2: a(n) = 2^n. / Comment

A000110

Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes. / Comment

A000142

Factorial numbers: n! = 1*2*3*4*...*n (order of symmetric group S_n, number of permutations of n letters). / Comment

A000244

Powers of 3. / Comment

A000258

E.g.f.: exp(exp(exp(x)-1)-1). / Comment

A000262

Number of "sets of lists": number of partitions of {1,..,n} into any number of lists, where a list means an ordered subset. / Comment

A000295

Eulerian numbers 2^n - n - 1. (Column 2 of Euler's triangle A008292.) / Comment

A000302

Powers of 4. / Comment

A000312

Number of labeled mappings from n points to themselves (endofunctions): n^n. / Comment

A000392

Stirling numbers of second kind S(n,3). / Comment

A000522

Total number of arrangements of a set with n elements: a(n) = Sum_{k=0..n} n!/k!. / Comment

A000601

Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)). / Comment

A000670

Number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements. / Comment

A008302

Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product (1+x+...+x^k); k=0..n. / Comment

A001339

a(n) = Sum (k+1)! C(n,k), k = 0..n. / Comment

A001399

Number of partitions of n into at most 3 parts; also partitions of n+3 in which the greatest part is 3; also multigraphs with 3 nodes and n edges. / Comment

A001970

Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence. / Comment

A002597

A generalized partition function. / Comment

A002620

Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4). / Comment

A002623

G.f.: 1/((1-x)^3*(1-x^2)). / Comment

A002866

a(0) = 1; for n>0, a(n) = 2^(n-1)*n!. / Comment

A004250

Number of graphical partitions of 2n. / Comment

A006128

Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n. / Comment

A007318

Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0<=k<=n. / Comment

A007526

a(n) = n(a(n-1) + 1). / Comment

A008275

Triangle read by rows of Stirling numbers of first kind, s(n,k), n >= 1, 1<=k<=n. / Comment

A008277

Triangle of Stirling numbers of 2nd kind, S2(n,k), n >= 1, 1<=k<=n. / Comments

A014968

Expansion of (1/theta_4 - 1)/2. / Comment

A025168

E.g.f.: exp(x/(1-2*x)). / Comment

A034001

One third of triple factorial numbers. / Comment

A034691

Euler transform of powers of 2 [ 1,2,4,8,16,... ].

A034899

Euler transform of powers of 2 [ 2,4,8,16,... ]. / Comment

A049611

a(n)=T(n,2), array T as in A049600. / Comment

A050351

Number of 3-level labeled linear rooted trees with n leaves. / Comment

A055887

Number of ordered partitions of partitions. / Comment

A058694

Partial products p(0)*p(1)*...*p(n) of partition numbers A000041. / Comment

A057524

Number of 3 x n binary matrices without unit columns up to row and column permutations. / Comment

A058681

Number of matroids of rank 2 on n labeled points. / Comment

A064350

(3n)!/n!. / Comment

A064618

Stirling transform of (n!)^2. / Comment

A066186

Sum of (the zero-th moments of) all partitions of n. / Comment

A075729

Number of different hierarchical orderings that can be formed from n labeled elements: these are divided into groups and the elements in each group are then arranged in a "preferential arrangement" or "weak order" as in A000670.

A075744

Hierarchies of hierarchies. / Comment

A077585

2^(2^n-1)-1. / Comment

A083355

Number of ordered compositions of compositions.

A084362

a(n) = Sum{j_1 + ... + j_n = n} Sum_{k=1..n} k*C(n-1,k-1), where the outer sum is over all partitions of n.

A089378

Number of one-step transitions between all unlabeled hierarchies of n elements.

A093694

Number of one-element transitions from the partitions of n to the partitions of n+1 for labeled parts.

A093695

Number of one-element transitions among partitions of the integer n for unlabeled parts.

A094251

Number of one-element transitions between all set partitions of n labeled elements.

A094533

Number of one-element transitions among partitions of the integer n for labeled parts.

A096541

Number of parts unequal to 1 in all partitions of the integer n. Also the difference between the labeled and the unlabeled case of one-element transitions from the partitions of n to the partitions of n+1.

A096586

Number of one-element transitions among all integer partitions of the integers from m=0 to m=n in the unlabeled case.

A097236

Number of hierachical orderings ("societies") with at least 2 elements ("individuals") on each level for n labeled elements.

A097237

Number of hierarchical orderings ("societies") of n labeled elements ("individuals") with at least two occupied levels.

A097391

The number of hierarchies with at least one subhierarchy composed of exactly 2 levels and no subhierarchiy with more than 2 levels.

A097392

The number of hierarchies with at least one subhierarchy composed of exactly 3 levels and no subhierarchy with more than 3 levels.

A098407

Number of different hierarchical orderings that can be formed from n unlabeled elements with no repetition of subhierarchies.

A099880

Number of preferential arrangements (or simple hierarchies) of 2*n labeled elements with two kinds of elements (where each kind has n elements).

A101052

Number of preferential arrangements of n labeled elements when only k<=3 ranks are allowed.

A101109

Number of sets of lists (sequences) of n labeled elements with k=3 elements per list.

A102232

Number of preferential arrangements of n labeled elements when at least k=three ranks are required.

A102233

Number of preferential arrangements of n labeled elements when at least k=3 elements per rank are required.

A102420

Number of partitions of n with exactly k = 5 parts and each part p <= 5.

A102422

Number of partitions of n with k <= 5 parts and each part p <= 5.

A102424

Number of partitions of n with each part p <= 5 and each part's multiplicity m <= 5.

A103446

Unlabeled analog of A025168.

A104249

(3*n^2+n+2)/2.

A104460

Number of hierarchical orderings for n unlabeled elements with 2 possible classes for levels l>=2. Consider a hierarchical ordering of n unlabeled elements into groups as defined in A034691. In addition assume that each level l with l >= 2 can fall into one of two classes A and B. Let | be a separator among different groups and let : be a separator between levels. Furthermore, let * denote an unlabeled element which is written as "a" if it falls into class A and as "b" if it falls into class B. As an example with n=4 one can have *|*:ab. In this example one has two groups, where the second group has tree elements, one on level l=1 and two on level l=2. One of the two elements on l=2 belongs to class A, the other to class B.

+21
4

A104500

Number of different groupings among the hierarchical orderings of n unlabeled elements.

A104525

Number of hierarchical orderings of n unlabeled elements where levels are clustered. Consider a hierarchical ordering as defined in A034691 where n unlabeled elements are divided into groups and the elements in each group are then arranged in a "preferential arrangement" as in A000079. Now introduce an additional grouping among the levels. One could speak of "frames" which cluster levels.

A104533

Number of hierarchical orderings for n labeled elements (see A075729) but there are two kinds A and B of elements.

A107894

Sum over the products of factorials of parts in all partitions of n where the sum runs over the number of different parts only.

A107895

Euler transform of n!.

A108492

Sum of NumberOfParts!/NumberOfDifferentParts! for all integer partitions of n.

A109092

Number of hierarchical orderings for n labeled elements with 2 possible classes A and B for levels l>=2. Labeled analogue of A104460.

A109186

Number of hierarchical orderings of n unlabeled elements where levels are clustered. Labeled analogue of A104525.

A109509

Number of hierachical orderings with at least 2 elements on each level for n unlabeled elements. Unlabeled analogue of A097236.

A110045

Number of hierarchical orderings ("societies") of n unlabeled elements ("individuals") with at least two occupied levels.

A119800

Array of coordination sequences for cubic lattices (rows) and of numbers of L1 forms in cubic lattices (columns) (array read by antidiagonals).

A120672

Consider a set A containing at least n-1 elements of sort "a" and a set B containing at least n-1 elements of sort "b". From set A we take i elements, from set B we take (n-i) elements such that i + (n-i) = n. Then we distribute these n elements in two urns L (left) and R (right). The order of selection among the two sorts counts. Equivalently we can say: Then we form two sequences L and R from these n elements. The position of the sort of the elements within the sequences counts. Furthermore, the occupations of the urns are permuted. In other words, the order of the sequences L and R is swaped from L|R to R|L. For n=3 we have a(n=3)=12 configurations [L|R] and [R|L]: [aaa|b], [b|aaa], [baa|a], [a|baa], [aba|a], [a|aba], [aab|a], [a|aab].and [bbb|a], [a|bbb], [abb|b], [b|abb], [bab|b], [b|bab], [bba|b], [b|bba].

A120928

Number of "ups" and "downs" in the permutations of [n] if either a previous counted "up" ("down") or a "void" proceeds an "up" ("down") which then will be counted also. An "up" ("down") is a neighboring pair of elements e_i, e_j of [n] with e_i < e_j (e_i > e_j). A "void" is a missing preceding pair, i.e. the start of [n]. We discus two examples for [n=4]. In the permutation [3, 1, 2, 4] "void" proceeds the pair 3,1 and consequently a "down" is counted. No "up" which has been counted proceeds the "ups" 1,2 and 2,4 so they are not counted. In [3, 4, 1, 2] the "up" 3,4 is counted and so is the next "up" 1,2 but the down 4,1 has no preceding "down" registered and is therefore not counted.

A121306

Array read by antidiangonals: a(m,n) = a(m,n-1)+a(m-1,n) but with initialization values a(0,0)=0, a(m>=1,0)=1, a(0,1)=1, a(0,n>1)=0.

A121547

Fourth slice along the 1-2-plane in the cube a(m,n,o) = a(m-1,n,o)+a(m,n-1,o)+a(m,n,o-1) for which the first sclice is Pascal's triangle (slice read by anti-diagonals).

A121662

Triangle read by rows: T(i,j) for the recurrence T(i,j)=(T(i-1)+1,j)*i.

A121682

Triangle read by rows: T(i,j)=(T(i-1)+i,j)*i.

A122218

Pascal array A(n,p,k) for selection of k elements from two sets L and U with n elements in total whereat the nl = n - p elements in L are labeled and the nu = p elements in U are unlabeled and (in this example) with p = 2 (read by rows).

A122404

Number of preferential arrangements of n labeled elements where the exchange of elements among the levels is restricted to levels of different occupation numbers.

A122768

Number of combinations which can be taken from the integer partitions of n. Total number of cases in the (n,m)-fragmentation process.

A126350

Triangle read by rows: matrix product of the binomial coefficients with the Stirling numbers of the second kind.

A126351

Triangle read by rows: matrix product of the Stirling numbers of the second kind with the binomial coefficients.

A126352

Triangle read by rows: matrix product of the binomial coefficients with the Stirling numbers of the first kind.

A126353

Triangle read by rows: matrix product of the Stirling numbers of the first kind with the binomial coefficients.

A128012

3*A001399(n).

A129247

Invert transform of the Bell numbers..

A131407

Repeated set partitions or nested set partitions. Possible coalitions among n persons.

A131408

Repeated integer partitions or nested integer partitions.

A131965

a(n) = a(n) = 1 + sum_{i=2}^{n-1} n * a(i).

A133998

The number of isomers of soccerball C_60H_n Buckminster fullerene.

A134686

Number of social welfare functions according to the definition given by Kim and Roush for m=n, where m = number of persons and n = number of alternatives.

A135084

a(n) = A000110(2^n-1).

A135085

a(n) = A000110(2^n).

A133998

The number of isomers of soccerball C_60H_n Buckminster fullerene.

A136722

The number of isomers of soccerball C_60H_n Buckminster fullerene.

A136723

The number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.

A137591

Number of parenthesizings of products formed by n factors assuming noncommutativity and nonassociativity.

A137731

Repeated set splitting, labeled elements.

A137732

Repeated set splitting, unlabeled elements. Repeated integer partitioning into two parts.

A137736

Number of set partitions of n(n-1)/2.

A139359

Number L([n],m) of ways the labelled parts of each integer partition of n can be distributed into m nonempty labelled boxes.

A139415

Number of preferential arrangements (or hierarchical orderings) on the disconnected graphs on n unlabeled nodes.

A140585

Total number of all hierarchical orderings for all set partitions of n.

A141199

Number of hierarchical ordered partitions of partitions.

A141268

Number of phylogenetic rooted trees with n unlabeled objects.

A141799

Number of repeated integer partitions of n.

A143140

Total number of all repeated partitions of the n-set S={1,2,3,...,n}.

A143141

Total number of all repeated partitions of the integer n and its parts down to parts equal to 1.

A143463

Number of multiple hierarchies for n labeled elements.

A144791

N Euler transform of A141199.

A144792

EXP transform of A140585.

A153744

a(n) is the number of anti-hierarchical decompositions of an n-pyramidal hierarchy of n*(n+1)/2=A000217(n) labeled elements.

A158497

Triangle formed by the coordination sequences and the number of leaves for trees.

A158498

Triangle formed by C(n+k-1,k).

A165817

Number of compositions (= ordered integer partitions) of n into 2*n parts.

A165984

Number of ways to put n indistinguishable balls into n^3 distinguishable boxes.

A173009

The mean value m(n) = sum(k*p(n,k), k = 0 .. 2^n-n-1) of the distribution function p(n,k) := binomial(2^n-n-1, k)/2^(2^n-n-1).

A173010

The variance v(n) = sum((k-m(n))^2*p(n,k), k = 0 .. 2^n-n-1) of the distribution function p(n,k) := binomial(2^n-n-1, k)/2^(2^n-n-1).

A188667

Ordered (2,2)-selections from the multiset {1,1,2,2,3,3,...,n,n}.

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Manuskripte / Manuscripts

Unveröffentlichte Ergebnisse / Unpublished Results

Meine Programme / My Programs

Mathematik / Mathematics

1. MULTISELECTION

MULTISELECTION generates multiselections from multisets.

Maple worksheet Multiselection.mw Maple program Multiselection.mpl

Thomas Wieder: Generation of all possible multiselections from a multiset,
Progress in Applied Mathematics 2(1) (2011), 61 - 66.

2. ENUM

ENUM generates contingency tables with given shape and row and column sums.

Maple worksheet enum.mw Maple program enum.mpl

3. MULTICHOOSE and MULTISUBSET

Generate multiselections from multisets.

Maple worksheet for program multichoose.mw Maple program multichoose.mpl

Maple worksheet multisubset.mw Maple program multisubset

4. HANKEL

Evaluate the Hankel transform (Fortran).

HANKEL

T. Wieder: Numerical Hankel transform by the Fortran program HANKEL;
Transactions on Mathematical Software (TOMS) 25 (1999), 240 - 250.

5. OPTM0

Selection of optimal submultisets from a multiset.

OPTM0

Röntgenbeugung / X-Ray Diffraction:

1. DMRM

Two-dimensional deconvolution by Siska's method (Fortran).

DMRM

T. Wieder:
Iterative unfolding of two-dimensional data by Siska's method;
Journal of Applied Crystallography 34 (2001), 786.

2. GDSF

Evaluate the Generalized Debye Scattering Formula (Fortran).

GDSF

T. Wieder: A generalized Debye scattering formula and the Hankel transform;
Zeitschrift für Naturforschung 54a (1999), 124 - 130.

3. SBGBBG

X-ray Residual Stress Determination (Fortran).

SBGBBG SBGBB (Crystallography source code museum)

T. Wieder: SBGBBG, a program to evaluate the macroscopic strain/stress tensor of a polycrystalline sample from X-ray reflection positions;
Computer Physics Communication 85 (1995), 398 - 414.

4. WVM

Lattice Constants in Thin Films (Fortran).

WVM

T. Wieder: WVM: A computer program for the determination of lattice parameters and strains in thin films;
Computer Physics Communications 96 (1996), 53 - 60.

Materialia

1. Maple programs for the calculation (based on integer partitions) of some integer sequences of the OEIS.
Maple program MapleProgramsForSomeIntegerSequences.mpl

2. Some very basic combinatorial subroutines written in VBA for Excel.
VBA programs calculation of Binomial coefficients, Stirling numbers, Bell numbers, etc.

3. Some very basic combinatorial subroutines written for Maple (presently only very few...).
Maple programs Tupel.mpl etc.

4. A Maple program to calculate the number of k-combinations from a multiset according to MacMahon's formula.
Maple program MacMahonsMultisetFormula.mpl

5. Calculate the n-dimensional Surface Spherical Harmonics according to the definition by Harry Bateman.
Maple worksheet SSHY.mw Maple program Y.mpl Y.pdf