2018/12/24 by Yuval Hovannes Khachatryan-Raziel, Khachatryan-Raziel, Yuval Hovannes · 1 citation
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.1812.09863
A remarkable result of Stanley shows that the set of maximal chains in the non-crossing partition lattice of type A is Schur-positive, where descents are defined by a distinguished edge labeling. A bijection between these chains and labeled trees was presented by Goulden and Yong. Using Adin-Roichman's variant of Björner's EL-labeling, we show that the subset of maximal chains in the non-crossing partition lattice of type A, whose underlying tree is a convex caterpillar, is Schur-positive.