Rectangulotopes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908424317435904 |
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| author | Cardinal, Jean Pilaud, Vincent |
| author_facet | Cardinal, Jean Pilaud, Vincent |
| contents | Rectangulations are decompositions of a square into finitely many axis-aligned rectangles. We describe realizations of $(n-1)$-dimensional polytopes associated with two combinatorial families of rectangulations composed of $n$ rectangles. They are defined as quotientopes of natural lattice congruences on the weak Bruhat order on permutations in $\mathfrak{S}_n$, and their skeleta are flip graphs on rectangulations. We give simple vertex and facet descriptions of these polytopes, in particular elementary formulas for computing the coordinates of the vertex corresponding to each rectangulation, in the spirit of J.-L. Loday's realization of the associahedron. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rectangulotopes Cardinal, Jean Pilaud, Vincent Combinatorics Computational Geometry Discrete Mathematics 52B11, 52B12, 06B10, 05B45 Rectangulations are decompositions of a square into finitely many axis-aligned rectangles. We describe realizations of $(n-1)$-dimensional polytopes associated with two combinatorial families of rectangulations composed of $n$ rectangles. They are defined as quotientopes of natural lattice congruences on the weak Bruhat order on permutations in $\mathfrak{S}_n$, and their skeleta are flip graphs on rectangulations. We give simple vertex and facet descriptions of these polytopes, in particular elementary formulas for computing the coordinates of the vertex corresponding to each rectangulation, in the spirit of J.-L. Loday's realization of the associahedron. |
| title | Rectangulotopes |
| topic | Combinatorics Computational Geometry Discrete Mathematics 52B11, 52B12, 06B10, 05B45 |
| url | https://arxiv.org/abs/2404.17349 |