Segre powers of posets preserve EL-shellability
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912757496938496 |
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| author | Li, Yifei Sundaram, Sheila |
| author_facet | Li, Yifei Sundaram, Sheila |
| contents | For a bounded and graded poset $P$, we show that if $P$ is EL-shellable, then so is its $t$-fold Segre power $P^{(t)}=P\circ \cdots \circ P$ ($t$ factors), as defined by Björner and Welker [J. Pure Appl. Algebra, 198(1-3), 43--55 (2005)]. Our EL-labeling leads to formulas for the rank-selected invariants of $P^{(t)}$, generalising those given by Stanley for the subspace lattice [J. Combinatorial Theory Ser. A, 20(3):336-356, 1976]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Segre powers of posets preserve EL-shellability Li, Yifei Sundaram, Sheila Combinatorics Algebraic Topology 05E10, 05E05, 20C30, 55P99 For a bounded and graded poset $P$, we show that if $P$ is EL-shellable, then so is its $t$-fold Segre power $P^{(t)}=P\circ \cdots \circ P$ ($t$ factors), as defined by Björner and Welker [J. Pure Appl. Algebra, 198(1-3), 43--55 (2005)]. Our EL-labeling leads to formulas for the rank-selected invariants of $P^{(t)}$, generalising those given by Stanley for the subspace lattice [J. Combinatorial Theory Ser. A, 20(3):336-356, 1976]. |
| title | Segre powers of posets preserve EL-shellability |
| topic | Combinatorics Algebraic Topology 05E10, 05E05, 20C30, 55P99 |
| url | https://arxiv.org/abs/2512.10297 |