On the rook polynomial of grid polyominoes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918376582938624 |
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| author | Dinu, Rodica Navarra, Francesco |
| author_facet | Dinu, Rodica Navarra, Francesco |
| contents | Grid polyominoes form a class of thin polyominoes with one or more holes arranged in a grid-like pattern in the plane. In this paper, we prove that the rook polynomial of grid polyominoes coincides with the h-polynomial of their corresponding coordinate ring. Our approach is based on the theory of simplicial complexes and extends previous results for frame polyominoes, which are special cases of polyominoes with exactly one hole. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01818 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the rook polynomial of grid polyominoes Dinu, Rodica Navarra, Francesco Combinatorics Commutative Algebra 05B50, 05E40 Grid polyominoes form a class of thin polyominoes with one or more holes arranged in a grid-like pattern in the plane. In this paper, we prove that the rook polynomial of grid polyominoes coincides with the h-polynomial of their corresponding coordinate ring. Our approach is based on the theory of simplicial complexes and extends previous results for frame polyominoes, which are special cases of polyominoes with exactly one hole. |
| title | On the rook polynomial of grid polyominoes |
| topic | Combinatorics Commutative Algebra 05B50, 05E40 |
| url | https://arxiv.org/abs/2309.01818 |