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 42 articles , 1 standard article )

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  1. Savage, Carla D.: The mathematics of lecture hall partitions (2016)
  2. Stanley, Richard P.; Zanello, Fabrizio: Some asymptotic results on $q$-binomial coefficients (2016)
  3. Radu, Cristian-Silviu: An algorithmic approach to Ramanujan-Kolberg identities (2015)
  4. Xin, Guoce: A Euclid style algorithm for MacMahon’s partition analysis (2015)
  5. Chaubey, Sneha; Cheng, Wei; Malik, Amita; Zaharescu, Alexandru: On the parity of broken $k$-diamond partitions (2014)
  6. Konvalinka, Matjaž; Pak, Igor: Cayley compositions, partitions, polytopes, and geometric bijections (2014)
  7. Aparicio Monforte, Ainhoa; Kauers, Manuel: Formal Laurent series in several variables (2013)
  8. Beck, Matthias; Bliem, Thomas; Braun, Benjamin; Savage, Carla D.: Lattice point generating functions and symmetric cones (2013)
  9. Beck, Matthias; Braun, Benjamin; Le, Nguyen: Mahonian partition identities via polyhedral geometry (2013)
  10. Konvalinka, Matjaž; Pak, Igor: Triangulations of Cayley and Tutte polytopes (2013)
  11. Boumova, Silvia; Drensky, Vesselin: Cocharacters of polynomial identities of upper triangular matrices. (2012)
  12. Du, Daniel K.; Hou, Qing-Hu: Partially ordinal sums and $P$-partitions (2012)
  13. Bedratyuk, Leonid; Xin, Guoce: MacMahon partition analysis and the Poincaré series of the algebras of invariants of ternary and quaternary forms (2011)
  14. Xiong, Xinhua: Two congruences involving Andrews-Paule’s broken 3-diamond partitions and 5-diamond partitions (2011)
  15. Beck, Matthias; Gessel, Ira M.; Lee, Sunyoung; Savage, Carla D.: Symmetrically constrained compositions (2010)
  16. Andrews, George E.: The meaning of Ramanujan now and for the future (2009)
  17. Gao, Wei; Hou, Qing-Hu; Xin, Guoce: On $P$-partitions related to ordinal sums of posets (2009)
  18. Garsia, Adriano; Musiker, Gregg; Wallach, Nolan; Xin, Guoce: Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems (2009)
  19. Garsia, A.; Wallach, N.; Xin, G.; Zabrocki, M.: Hilbert series of invariants, constant terms and Kostka-Foulkes polynomials (2009)
  20. Rødseth, Øystein J.; Sellers, James A.; Tverberg, Helge: Enumeration of the degree sequences of non-separable graphs and connected graphs (2009)

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