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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 *s*_{λ}(*m*+*y*_{1},...,*m*+*y*_{n}). 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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