MacMahon's ${\Omega }_{\ge }$ operator: A computational framework

Abstract

MacMahon introduced partition analysis in his book ``Combinatory Analysis'' as a computational technique for solving problems related to systems of linear Diophantine equations and inequalities. This paper aims to develop a fundamental computational method for MacMahon's partition analysis. As applications, we present simplified computations for ``Han's formula'', the ``$k$-gon partitions problem'', and the ``two-dimensional problem''. Moreover, we apply our method to solve a challenging problem.

19 pages

References in corpus (1)

• A Euclid style algorithm for MacMahon's partition analysis