MacMahon's $Ω_\geq$ operator: A computational framework
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917151601852416 |
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| author | Liu, Feihu Xin, Guoce |
| author_facet | Liu, Feihu Xin, Guoce |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MacMahon's $Ω_\geq$ operator: A computational framework Liu, Feihu Xin, Guoce Combinatorics 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. |
| title | MacMahon's $Ω_\geq$ operator: A computational framework |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.15355 |