A visual approach to symmetric chain decompositions of finite Young lattices

2024/07/29 by Terrance Coggins, Coggins, Terrance, Robert W. Donley +5 · 1 citation
Computer Science · #05A17 06A07 #Combinatorics (math.CO) #Data Management and Algorithms #Data Visualization and Analytics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2407.20008

openalex publication_date 2024/07/29 · openalex created_date 2024/08/01 · openalex updated_date 2026/07/28

Abstract

The finite Young lattice L(m, n) is rank-symmetric, rank-unimodal, and has the strong Sperner property. R. Stanley further conjectured that L(m, n) admits a symmetric chain order. We show that the order structure on L(m, n) is equivalent to a natural ordering on the lattice points of a dilated n-simplex, which in turn corresponds to a weight diagram for the root system of type A_n. Lindstr" om's symmetric chain decompositions for L(3, n) are described completely through pictures.

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