Triangulations of simplices with vanishing local h-polynomial
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866913634641248256 |
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| author | de Moura, André Gunther, Elijah Payne, Sam Schuchardt, Jason Stapledon, Alan |
| author_facet | de Moura, André Gunther, Elijah Payne, Sam Schuchardt, Jason Stapledon, Alan |
| contents | Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we identify a class of refinements that preserve the local h-polynomial. In dimensions 2 and 3, we show that all triangulations with vanishing local h-polynomial are obtained from one or two simple examples by a sequence of such refinements. In higher dimensions, we prove some partial results and give further examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_10843 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Triangulations of simplices with vanishing local h-polynomial de Moura, André Gunther, Elijah Payne, Sam Schuchardt, Jason Stapledon, Alan Combinatorics 05E45, 52B70 Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we identify a class of refinements that preserve the local h-polynomial. In dimensions 2 and 3, we show that all triangulations with vanishing local h-polynomial are obtained from one or two simple examples by a sequence of such refinements. In higher dimensions, we prove some partial results and give further examples. |
| title | Triangulations of simplices with vanishing local h-polynomial |
| topic | Combinatorics 05E45, 52B70 |
| url | https://arxiv.org/abs/1909.10843 |