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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2602.04533 |
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| _version_ | 1866908812961644544 |
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| author | Cheon, Gi-Sang Choi, Hong Joon Kwon, Gukwon Lee, Hojoon Wang, Yaling |
| author_facet | Cheon, Gi-Sang Choi, Hong Joon Kwon, Gukwon Lee, Hojoon Wang, Yaling |
| contents | We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a unified treatment of Birkhoff problem on non-isomorphic posets and Dedekind problem on antichains. A key idea is a systematic construction and indexing of poset matrices as principal submatrices of the binary Pascal matrix, leading to new structural insights through permutation similarity and domination relations. This approach provides a consistent matrix-based perspective on classical enumeration problems in poset theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04533 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A matrix approach to the structure, enumeration, and applications of partially ordered sets Cheon, Gi-Sang Choi, Hong Joon Kwon, Gukwon Lee, Hojoon Wang, Yaling Combinatorics We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a unified treatment of Birkhoff problem on non-isomorphic posets and Dedekind problem on antichains. A key idea is a systematic construction and indexing of poset matrices as principal submatrices of the binary Pascal matrix, leading to new structural insights through permutation similarity and domination relations. This approach provides a consistent matrix-based perspective on classical enumeration problems in poset theory. |
| title | A matrix approach to the structure, enumeration, and applications of partially ordered sets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.04533 |