Macmahon's partition analysis IX:K-gon partitions

2001/10/01 by George E. Andrews, Peter Paule, Axel Riese · 5 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.1017/s0004972700039988

Abstract

Dedicated to George Szekeres on the occasion of his 90th birthday MacMahon devoted a significant portion of Volume II of his famous book Combinatory Analysis to the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon's method turns into an extremely powerful tool when implemented in computer algebra. In this note we explain how the use of the package Omega developed by the authors has led to a generalisation of a classical counting problem related to triangles with sides of integer length.

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• MacMahon's partition analysis XII: Plane partitions
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• MacMahon's Ω_≥ operator: A computational framework
• Partitions and Compositions defined by inequalities
• Polyhedral Omega: A New Algorithm for Solving Linear Diophantine Systems

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• MacMahon's partition analysis XII: Plane partitions
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