Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity
Combinatorics
2025-06-03 v1
Abstract
We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized Littlewood--Richardson coefficients for Temperley--Lieb immanants of Jacobi--Trudi matrices. We will also show that our rule behaves well with Bender--Knuth involutions, recovering the symmetry of Littlewood--Richardson coefficients. As an application, we use our rule to prove a special case of a Schur log-concavity conjecture by Lam--Postnikov--Pylyavskyy.
Keywords
Cite
@article{arxiv.2506.00349,
title = {Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity},
author = {Chau Nguyen and Son Nguyen and Dora Woodruff},
journal= {arXiv preprint arXiv:2506.00349},
year = {2025}
}