Séminaire Lotharingien de Combinatoire, 95B.21 (2026), 12 pp.
Chau Nguyen, Son Nguyen and Dora Woodruff
Shuffle Tableaux, Littlewood-Richardson Coefficients, and Schur Log-Concavity
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.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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