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Proof of a Positivity Conjecture on Schur Functions
symmetric function Schur function multiplier sequence totally positive sequence
2014/6/3
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t)n denote the rising factorial, and let ΛR denote the a...
Schur Positivity and the q-Log-convexity of the Narayana Polynomials
q-log-concavity q-log-convexity q-Narayana number Narayana polynomial lattice permutation Schur positivity Littlewood-Richardson rule
2014/6/3
Using Schur positivity and the principal specialization of Schur functions, we provide a proof of a recent conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials, and a proof of...