Bijection between trees in Stanley character formula and factorizations of a cycle

DOI10.37236/11577arXiv2210.04478MaRDI QIDQ6117432

Karolina Trokowska, Piotr Śniady

Publication date: 19 February 2024

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.04478

zbMATH Keywords

symmetric groupsirreducible complex charactersYoung diagramshook lengthsnormalized characterspartitions of rectangular shape

Mathematics Subject Classification ID

Trees (05C05) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Paths and cycles (05C38) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Cites Work

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• Stanley's formula for characters of the symmetric group.
• Combinatorial interpretation and positivity of Kerov's character polynomials
• Two positivity conjectures for Kerov polynomials
• Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
• Representations of symmetric groups and free probability
• Irreducible symmetric group characters of rectangular shape.
• Stanley's character polynomials and coloured factorisations in the symmetric group
• Minimal factorizations of a cycle and central multiplicative functions on the infinite symmetric group
• Stanley character polynomials
• Combinatorics of asymptotic representation theory
• An explicit form for Kerov's character polynomials
• The algebra of conjugacy classes in symmetric groups, and partial permutations