Top homology of hypergraph matching complexes, $p$-cycle complexes and Quillen complexes of symmetric groups

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dc.creatorShareshian, John
dc.creatorWachs, Michelle L
dc.date2008-08-22
dc.date.accessioned2026-07-07T09:57:59Z
dc.date.available2026-07-07T09:57:59Z
dc.descriptionWe investigate the representation of a symmetric group $S_n$ on the homology of its Quillen complex at a prime $p$. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of $p$-uniform hypergraph matching complexes. We conjecture an explicit formula for the representation of $S_n$ on the top homology group of the corresponding hypergraph matching complex when $n \equiv 1 \bmod p$. Our conjecture follows from work of Bouc when $p=2$, and we prove the conjecture when $p=3$.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/0808.3114
dc.identifierhttp://arxiv.org/abs/0808.3114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167552
dc.subjectGroup Theory
dc.subjectCombinatorics
dc.subject20D30; 05E25
dc.titleTop homology of hypergraph matching complexes, $p$-cycle complexes and Quillen complexes of symmetric groups
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