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 54 articles , 1 standard article )

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  1. Andrews, George E.; Paule, Peter: MacMahon’s partition analysis XIII: Schmidt type partitions and modular forms (2022)
  2. Verreault, William: MacMahon partition analysis: a discrete approach to broken stick problems (2022)
  3. Braun, Lukas: Completing the classification of representations of (SL_n) with complete intersection invariant ring (2021)
  4. Francisco Neto, Antônio: An approach to isotropic tensor functions and their derivatives via omega matrix calculus (2020)
  5. Neto, Antônio Francisco: Matrix analysis and omega calculus (2020)
  6. Xin, Guoce; Zhong, Yueming: On parity unimodality of (q)-Catalan polynomials (2020)
  7. East, James; Niles, Ron: Integer polygons of given perimeter (2019)
  8. Francisco Neto, Antônio; Fonseca, Carolina Rodrigues: An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players (2019)
  9. Neto, Antônio Francisco: Generating functions of weighted voting games, MacMahon’s partition analysis, and Clifford algebras (2019)
  10. Ono, Ken; Rolen, Larry: On Witten’s extremal partition functions (2019)
  11. Breuer, Felix; Zafeirakopoulos, Zafeirakis: Polyhedral omega: a new algorithm for solving linear Diophantine systems (2017)
  12. Savage, Carla D.: The mathematics of lecture hall partitions (2016)
  13. Stanley, Richard P.; Zanello, Fabrizio: Some asymptotic results on (q)-binomial coefficients (2016)
  14. Radu, Cristian-Silviu: An algorithmic approach to Ramanujan-Kolberg identities (2015)
  15. Xin, Guoce: A Euclid style algorithm for MacMahon’s partition analysis (2015)
  16. Chaubey, Sneha; Cheng, Wei; Malik, Amita; Zaharescu, Alexandru: On the parity of broken (k)-diamond partitions (2014)
  17. Konvalinka, Matjaž; Pak, Igor: Cayley compositions, partitions, polytopes, and geometric bijections (2014)
  18. Aparicio Monforte, Ainhoa; Kauers, Manuel: Formal Laurent series in several variables (2013)
  19. Beck, Matthias; Bliem, Thomas; Braun, Benjamin; Savage, Carla D.: Lattice point generating functions and symmetric cones (2013)
  20. Beck, Matthias; Braun, Benjamin; Le, Nguyen: Mahonian partition identities via polyhedral geometry (2013)

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