MacMahon's ≥ 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.
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