Geometric view of interval poset permutations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912613922766848 |
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| author | Bagno, Eli Eisenberg, Estrella Reches, Shulamit Sigron, Moriha |
| author_facet | Bagno, Eli Eisenberg, Estrella Reches, Shulamit Sigron, Moriha |
| contents | In a recent study by Tenner, the concept of the interval poset of a permutation was introduced to effectively represent all intervals and their inclusions within a permutation. In this paper, we present a new geometric viewpoint on interval posets. We establish a one-to-one correspondence between the set of interval posets for permutations of size n and a specific subset of dissections of a convex polygon with n sides. Through this correspondence, we investigate various intriguing subsets of interval posets and uncover their connections with specific polygon dissections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric view of interval poset permutations Bagno, Eli Eisenberg, Estrella Reches, Shulamit Sigron, Moriha Combinatorics In a recent study by Tenner, the concept of the interval poset of a permutation was introduced to effectively represent all intervals and their inclusions within a permutation. In this paper, we present a new geometric viewpoint on interval posets. We establish a one-to-one correspondence between the set of interval posets for permutations of size n and a specific subset of dissections of a convex polygon with n sides. Through this correspondence, we investigate various intriguing subsets of interval posets and uncover their connections with specific polygon dissections. |
| title | Geometric view of interval poset permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.13193 |