Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity
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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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Cited by 4 Pith papers
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L-log-concavity and a proof of the conjecture of Lam, Postnikov and Pylyavskyy
The Lam-Postnikov-Pylyavskyy conjecture is proven by introducing skeps as a combinatorial model for Littlewood-Richardson coefficients and establishing their L-log-concavity via Murota's theory.
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Temperley-Lieb Immanants of Ribbon Decomposition Matrices
Temperley-Lieb immanants are Schur-positive on ribbon decomposition matrices, extending known Jacobi-Trudi cases, with a conjecture for the full dual canonical basis.
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Temperley-Lieb Immanants of Ribbon Decomposition Matrices
Temperley-Lieb immanants are Schur-positive on ribbon decomposition matrices, generalizing Haiman's Jacobi-Trudi result, with a conjecture for the full dual canonical basis.
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Temperley-Lieb Immanants of Ribbon Decomposition Matrices
Proves Schur-positivity of Temperley-Lieb immanants on ribbon decomposition matrices and conjectures the property for the full dual canonical basis.
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