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

Fuente: arXiv
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Autores principales: Trokowska, Karolina, Śniady, Piotr
Formato: Preprint
Publicado: 2022
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author Trokowska, Karolina
Śniady, Piotr
author_facet Trokowska, Karolina
Śniady, Piotr
contents Stanley and Féray gave a formula for the irreducible character of the symmetric group related to a multi-rectangular Young diagram. This formula shows that the character is a polynomial in the multi-rectangular coordinates and gives an explicit combinatorial interpretation for its coefficients in terms of counting certain decorated maps (i.e., graphs drawn on surfaces). In the current paper we concentrate on the coefficients of the top-degree monomials in the Stanley character polynomial, which corresponds to counting certain decorated plane trees. We give an explicit bijection between such trees and minimal factorizations of a cycle.
format Preprint
id arxiv_https___arxiv_org_abs_2210_04478
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Bijection between trees in Stanley character formula and factorizations of a cycle
Trokowska, Karolina
Śniady, Piotr
Combinatorics
05A19 (Primary) 05C05 (Secondary)
Stanley and Féray gave a formula for the irreducible character of the symmetric group related to a multi-rectangular Young diagram. This formula shows that the character is a polynomial in the multi-rectangular coordinates and gives an explicit combinatorial interpretation for its coefficients in terms of counting certain decorated maps (i.e., graphs drawn on surfaces). In the current paper we concentrate on the coefficients of the top-degree monomials in the Stanley character polynomial, which corresponds to counting certain decorated plane trees. We give an explicit bijection between such trees and minimal factorizations of a cycle.
title Bijection between trees in Stanley character formula and factorizations of a cycle
topic Combinatorics
05A19 (Primary) 05C05 (Secondary)
url https://arxiv.org/abs/2210.04478