MacMahon's $Ω_\geq$ operator: A computational framework

Feihu Liu; Guoce Xin

doi:10.1016/j.jsc.2026.102608

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arXiv · 2512.15355

MacMahon's $Ω_\geq$ operator: A computational framework

Feihu Liu·Guoce Xin

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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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BibTeX RIS

Feihu Liu, Guoce Xin. 2025-12-17. MacMahon's $Ω_\geq$ operator: A computational framework. https://doi.org/10.1016/j.jsc.2026.102608

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