Permutation ensembles and acyclicity on product of simplices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910946215067648 |
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| author | Oh, SuHo |
| author_facet | Oh, SuHo |
| contents | We propose the study of $S_n$-ensembles: $n \times n$ arrays of permutations of $[n]$ that encode the boundary data of $nΔ_{n-1}$. We characterize precisely when an $S_4$-ensemble contains a permutation appearing exactly four times, leading to a complete description of the types of boundary of $4Δ_3$ that can be extended to fine mixed subdivisions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutation ensembles and acyclicity on product of simplices Oh, SuHo Combinatorics 05B35, 05B45, 05E45, 52B05 We propose the study of $S_n$-ensembles: $n \times n$ arrays of permutations of $[n]$ that encode the boundary data of $nΔ_{n-1}$. We characterize precisely when an $S_4$-ensemble contains a permutation appearing exactly four times, leading to a complete description of the types of boundary of $4Δ_3$ that can be extended to fine mixed subdivisions. |
| title | Permutation ensembles and acyclicity on product of simplices |
| topic | Combinatorics 05B35, 05B45, 05E45, 52B05 |
| url | https://arxiv.org/abs/2504.21149 |