Interval Posets and Polygon Dissections
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914846928273408 |
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| author | Bagno, Eli Eisenberg, Estrella Reches, Shulamit Sigron, Moriah |
| author_facet | Bagno, Eli Eisenberg, Estrella Reches, Shulamit Sigron, Moriah |
| contents | The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval posets of permutations. We present a bijection between tree interval posets and convex polygons with non-crossing diagonals, offering a novel geometric perspective on this purely combinatorial concept. Additionally, we provide an enumeration of interval posets using this bijection and demonstrate its application to block-wise simple permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interval Posets and Polygon Dissections Bagno, Eli Eisenberg, Estrella Reches, Shulamit Sigron, Moriah Discrete Mathematics The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval posets of permutations. We present a bijection between tree interval posets and convex polygons with non-crossing diagonals, offering a novel geometric perspective on this purely combinatorial concept. Additionally, we provide an enumeration of interval posets using this bijection and demonstrate its application to block-wise simple permutations. |
| title | Interval Posets and Polygon Dissections |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2406.16392 |