Subdivisions of lower Eulerian posets
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909915651506176 |
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| author | Stapledon, Alan |
| author_facet | Stapledon, Alan |
| contents | There is a natural notion of a subdivision of a lower Eulerian poset called a strong formal subdivision, which abstracts the notion of a polyhedral subdivision of a polytope, or a proper, surjective morphism of fans. We show that there is a canonical bijection between strong formal subdivisions and triples consisting of a lower Eulerian poset, a corresponding rank function, and a non-minimal element such that the join with any other element exists. The bijection uses the non-Hausdorff mapping cylinder construction introduced by Barmak and Minian. A corresponding bijection for $CW$-posets is given, as well as an application to computing the $cd$-index of an Eulerian poset. A companion paper explores applications to Kazhdan-Lusztig-Stanley theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_16608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subdivisions of lower Eulerian posets Stapledon, Alan Combinatorics 06A07 There is a natural notion of a subdivision of a lower Eulerian poset called a strong formal subdivision, which abstracts the notion of a polyhedral subdivision of a polytope, or a proper, surjective morphism of fans. We show that there is a canonical bijection between strong formal subdivisions and triples consisting of a lower Eulerian poset, a corresponding rank function, and a non-minimal element such that the join with any other element exists. The bijection uses the non-Hausdorff mapping cylinder construction introduced by Barmak and Minian. A corresponding bijection for $CW$-posets is given, as well as an application to computing the $cd$-index of an Eulerian poset. A companion paper explores applications to Kazhdan-Lusztig-Stanley theory. |
| title | Subdivisions of lower Eulerian posets |
| topic | Combinatorics 06A07 |
| url | https://arxiv.org/abs/2511.16608 |