Lecture hall tableaux
| Autor: | Corteel, Sylvie, Kim, Jang Soo |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 25 pages, 5 figures, to appear in Adv. Math |
| Databáze: | arXiv |
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