Omega

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.


References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Stanley, Richard P.; Zanello, Fabrizio: Some asymptotic results on $q$-binomial coefficients (2016)
  2. Radu, Cristian-Silviu: An algorithmic approach to Ramanujan-Kolberg identities (2015)
  3. Xin, Guoce: A Euclid style algorithm for MacMahon’s partition analysis (2015)
  4. Aparicio Monforte, Ainhoa; Kauers, Manuel: Formal Laurent series in several variables (2013)
  5. Beck, Matthias; Braun, Benjamin; Le, Nguyen: Mahonian partition identities via polyhedral geometry (2013)
  6. Boumova, Silvia; Drensky, Vesselin: Cocharacters of polynomial identities of upper triangular matrices. (2012)
  7. Du, Daniel K.; Hou, Qing-Hu: Partially ordinal sums and $P$-partitions (2012)
  8. Bedratyuk, Leonid; Xin, Guoce: MacMahon partition analysis and the Poincaré series of the algebras of invariants of ternary and quaternary forms (2011)
  9. Beck, Matthias; Gessel, Ira M.; Lee, Sunyoung; Savage, Carla D.: Symmetrically constrained compositions (2010)
  10. Andrews, George E.: The meaning of Ramanujan now and for the future (2009)
  11. Gao, Wei; Hou, Qing-Hu; Xin, Guoce: On $P$-partitions related to ordinal sums of posets (2009)
  12. Garsia, Adriano; Musiker, Gregg; Wallach, Nolan; Xin, Guoce: Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems (2009)
  13. Garsia, A.; Wallach, N.; Xin, G.; Zabrocki, M.: Hilbert series of invariants, constant terms and Kostka-Foulkes polynomials (2009)
  14. Davis, J.William; D’Souza, Erwin; Lee, Sunyoung; Savage, Carla D.: Enumeration of integer solutions to linear inequalities defined by digraphs (2008)
  15. Ekhad, Shalosh B.; Zeilberger, Doron: Using Rota’s Umbral calculus to enumerate Stanley’s $P$-partitions (2008)
  16. Xin, Guoce: Constructing all magic squares of order three (2008)
  17. Andrews, George E.; Sellers, James A.: On Sloane’s generalization of non-squashing stacks of boxes (2007)
  18. Bóna, Miklós; Ju, Hyeong-Kwan; Yoshida, Ruriko: On the enumeration of certain weighted graphs (2007)
  19. Corteel, Sylvie; Lee, Sunyoung; Savage, Carla D.: Five guidelines for partition analysis with applications to lecture hall-type theorems (2007)
  20. Heuberger, Clemens; Prodinger, Helmut: The Hamming weight of the non-adjacent-form under various input statistics (2007)

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