Omega swMATH ID: 11878 Software Authors: Andrews, George E.; Paule, Peter; Riese, Axel Description: Omega is a Mathematica implementation of MacMahon’s Partition Analysis carried out by Axel Riese, a Postdoc of the RISC Combinatorics group. It has been developed together with George E. Andrews and Peter Paule within the frame of a project initiated by Andrews on the occasion of his sabbatical at RISC in spring 1998. Partition Analysis is a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations, respectively. But as a matter of fact, MacMahon’s ideas have not received due attention with the exception of work by Richard Stanley. The object of the Omega project is to change this situation by demonstrating the power of MacMahon’s method in current combinatorial research. Homepage: http://www.risc.jku.at/research/combinat/software/ergosum/RISC/Omega.html Dependencies: Mathematica Keywords: partitions; Omega calculus Related Software: OEIS; LattE; Mathematica; CliffOC; CliffSymNil; CliffMath; RotaStanley; mftoolbox; Maple; QEta; SINGULAR; barvinok; TOPCOM; SageMath; Normaliz; polymake; PPar; ROTA; MAYLIS; USAW Cited in: 55 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year MacMahon’s partition analysis: The Omega package. Zbl 0979.05008Andrews, George E.; Paule, Peter; Riese, Axel 2001 all top 5 Cited by 64 Authors 10 Andrews, George Eyre 8 Paule, Peter 7 Riese, Axel 7 Xin, Guoce 6 Savage, Carla D. 5 Neto, Antônio Francisco 3 Beck, Matthias 3 Corteel, Sylvie 3 Lee, Sunyoung 3 Sellers, James Allen 2 Braun, Benjamin 2 Garsia, Adriano M. 2 Hou, Qinghu 2 Konvalinka, Matjaž 2 Pak, Igor 2 Wallach, Nolan Russell 1 Aparicio-Monforte, Ainhoa 1 Bedratyuk, Leonid 1 Bliem, Thomas 1 Bóna, Miklós 1 Boumova, Silvia 1 Braun, Lukas 1 Breuer, Felix 1 Canfield, Rod 1 Chan, Song Heng 1 Chaubey, Sneha 1 Cheng, Wei 1 Davis, J. William 1 Drensky, Vesselin 1 D’Souza, Erwin 1 Du, Daniel K. 1 East, James 1 Ekhad, Shalosh B. (computer) 1 Fonseca, Carolina Rodrigues 1 Fu, Amy M. 1 Gessel, Ira Martin 1 Han, Guo-Niu 1 Heuberger, Clemens 1 Hitczenko, Paweł 1 Ju, Hyeong-Kwan 1 Kauers, Manuel 1 Lascoux, Alain 1 Malik, Amita 1 Mascioni, Vania 1 Musiker, Gregg 1 Niles, Ron 1 Ono, Ken 1 Prodinger, Helmut 1 Radu, Cristian-Silviu 1 Rødseth, Øystein J. 1 Rolen, Larry 1 Stanley, Richard Peter 1 Strehl, Volker 1 Tverberg, Helge Arnulf 1 Verreault, William 1 Xiong, Xinhua 1 Yoshida, Ruriko 1 Zabrocki, Mike 1 Zafeirakopoulos, Zafeirakis 1 Zaharescu, Alexandru 1 Zanello, Fabrizio 1 Zeilberger, Doron 1 Zhang, Zhizheng 1 Zhong, Yueming all top 5 Cited in 27 Serials 6 Discrete Mathematics 6 Journal of Combinatorial Theory. Series A 5 Annals of Combinatorics 4 Advances in Applied Mathematics 3 European Journal of Combinatorics 3 The Electronic Journal of Combinatorics 2 Bulletin of the Australian Mathematical Society 2 The Ramanujan Journal 1 Discrete Applied Mathematics 1 Linear and Multilinear Algebra 1 Periodica Mathematica Hungarica 1 Advances in Mathematics 1 Journal of Number Theory 1 Mathematics of Operations Research 1 Proceedings of the Japan Academy. Series A 1 Journal of Symbolic Computation 1 Annals of Operations Research 1 Journal of Elasticity 1 SIAM Review 1 Expositiones Mathematicae 1 Journal of Algebraic Combinatorics 1 Electronic Journal of Differential Equations (EJDE) 1 Transformation Groups 1 Integers 1 South East Asian Journal of Mathematics and Mathematical Sciences 1 Journal of Algebra and its Applications 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche all top 5 Cited in 19 Fields 48 Combinatorics (05-XX) 28 Number theory (11-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Convex and discrete geometry (52-XX) 5 Computer science (68-XX) 3 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Special functions (33-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year