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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.16612 |
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| _version_ | 1866914165783789568 |
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| author | Stapledon, Alan |
| author_facet | Stapledon, Alan |
| contents | In a companion paper, a canonical bijection was established between strong formal subdivisions of lower Eulerian posets 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 main goal of this paper is to relate the local $h$-polynomials of a strong formal subdivision to the Kazhdan-Lusztig-Stanley (KLS) invariants associated to its corresponding lower Eulerian poset under this bijection. As an application, we show that Braden and MacPherson's relative $g$-polynomials are alternative encodings of corresponding local $h$-polynomials. We also further develop equivariant KLS theory and give equivariant generalizations of our main results, as well as an application to equivariant Ehrhart theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subdivisions of lower Eulerian posets and KLS theory Stapledon, Alan Combinatorics 06A11 In a companion paper, a canonical bijection was established between strong formal subdivisions of lower Eulerian posets 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 main goal of this paper is to relate the local $h$-polynomials of a strong formal subdivision to the Kazhdan-Lusztig-Stanley (KLS) invariants associated to its corresponding lower Eulerian poset under this bijection. As an application, we show that Braden and MacPherson's relative $g$-polynomials are alternative encodings of corresponding local $h$-polynomials. We also further develop equivariant KLS theory and give equivariant generalizations of our main results, as well as an application to equivariant Ehrhart theory. |
| title | Subdivisions of lower Eulerian posets and KLS theory |
| topic | Combinatorics 06A11 |
| url | https://arxiv.org/abs/2511.16612 |