Séminaire Lotharingien de Combinatoire, 85B.25 (2021), 12 pp.
Karolina Wojtyniak
Bijection between Trees in Stanley Character Formula and Factorizations of a Cycle
Abstract.
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.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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