论文标题
Stanley角色公式中的树木之间的两者和一个周期的因素化
Bijection between trees in Stanley character formula and factorizations of a cycle
论文作者
论文摘要
斯坦利（Stanley）和费ray（Féray）为对称群体的不可约性特征提供了一个公式，该特征与多块状年轻图有关。该公式表明，该字符是多条件的多项式，在计数某些装饰的地图（即在表面上绘制的图形）方面，对其系数进行了明确的组合解释。在当前的论文中，我们集中于史丹利角色多项式中高级单位的系数，该系数与计算某些装饰的飞机树相对应。我们在此类树之间进行明确的培训和周期的最小化因素化。
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.
