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arXiv · 1804.02489

Lecture hall tableaux

Sylvie Corteel·Jang Soo Kim
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Abstract

We introduce lecture hall tableaux, which are fillings of a skew Young diagram satisfying certain conditions. Lecture hall tableaux generalize both lecture hall partitions and anti-lecture hall compositions, and also contain reverse semistandard Young tableaux as a limit case. We show that the coefficients in the Schur expansion of multivariate little $q$-Jacobi polynomials are generating functions for lecture hall tableaux. Using a Selberg-type integral we show that moments of multivariate little $q$-Jacobi polynomials, which are equal to generating functions for lecture hall tableaux of a Young diagram, have a product formula. We also explore various combinatorial properties of lecture hall tableaux.

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Sylvie Corteel, Jang Soo Kim. 2018-04-07. Lecture hall tableaux. https://arxiv.org/abs/1804.02489

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