Séminaire Lotharingien de Combinatoire, B81f (2020), 28 pp.

Sylvie Corteel and Jang Soo Kim

Enumeration of Bounded Lecture Hall Tableaux

Abstract. Recently the authors introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. In this paper, we enumerate bounded lecture hall tableaux. We show that their enumeration is closely related to standard and semistandard Young tableaux. We also show that the number of bounded lecture hall tableaux occurs as a coefficient in the Schur expansion of sλ(m+y1,...,m+yn). To prove this result, we use two main tools: non-intersecting lattice paths and bijections. In particular, we use ideas developed by Krattenthaler to prove bijectively the hook content formula.

Received: April 4, 2019. Accepted: November 6, 2019.

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