Journal of Combinatorics

Volume 14 (2023)

Number 2

Maximizing the Edelman–Greene statistic

Pages: 155 – 166

DOI: https://dx.doi.org/10.4310/JOC.2023.v14.n2.a1

Author

Gidon Orelowitz (Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, Il., U.S.A.)

Abstract

The Edelman–Greene statistic of S. Billey and B. Pawlowski measures the “shortness” of the Schur expansion of a Stanley symmetric function. We show that the maximum value of this statistic on permutations of Coxeter length $n$ is the number of involutions in the symmetric group $S_n$, and explicitly describe the permutations that attain this maximum. Our proof confirms a recent conjecture of C. Monical, B. Pankow, and A. Yong: we give an explicit combinatorial injection between certain collections of Edelman–Greene tableaux and standard Young tableaux.

Keywords

Edelman–Green tableau, standard young tableau, reduced decomposition

2010 Mathematics Subject Classification

05E10

Received 3 August 2021

Published 28 December 2022