Basic Hypergeometric Summations from Rook Theory

We establish discrete and continuous log-concavity results for a biparametric extension of the [Formula: see text]-numbers and of the [Formula: see text]-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our log-concavity results to the elliptic setting. One of our main ingredients is a putatively new lemma involving a multiplicative analogue of Turán’s inequality.

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Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients

Schlosser

Senapati

Uncu

2020

Int. J. Number Theory

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Basic Hypergeometric Summations from Rook Theory

Abstract: We employ a one-variable extension of q-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the q-Pfaff-Saalschütz summation and a 4φ3 summation by Jain.

Cited by 1 publication

References 24 publications

Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients

Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients

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