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arXiv · 2506.00349

Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity

Chau Nguyen·Son Nguyen·Dora Woodruff
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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.

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Chau Nguyen, Son Nguyen, Dora Woodruff. 2025-05-31. Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity. https://arxiv.org/abs/2506.00349

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