The commuting complex of the symmetric group with bounded number of p-cycles

2018/08/07 by Cihan Bahran, Bahran, Cihan
Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1808.02581

openalex publication_date 2018/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a fixed prime p, we consider a filtration of the commuting complex of elements of order p in the symmetric group \mathfrakS_n. The filtration is obtained by imposing successively relaxed bounds on the number of disjoint p-cycles in the cycle decomposition of the elements. We show that each term in the filtration becomes highly acyclic as n increases. We use FI-modules in the proof.

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