Zeilberger's KOH theorem and the strict unimodality of q-binomial coefficients

Authors

Fabrizio Zanello, Michigan Technological UniversityFollow

Document Type

Conference Proceeding

Publication Date

2-6-2015

Abstract

A recent nice result due to I. Pak and G. Panova is the strict unimodality of the -binomial coefficients . Since their proof used representation theory and Kronecker coefficients, the authors also asked for an argument that would employ Zeilberger's KOH theorem. In this note, we give such a proof. Then, as a further application of our method, we also provide a short proof of their conjecture that the difference between consecutive coefficients of can get arbitrarily large, when we assume that is fixed and is large enough.

Publisher's Statement

© Copyright 2015 American Mathematical Society. Publisher’s version of record: https://doi.org/10.1090/S0002-9939-2015-12510-5

Publication Title

Proceedings of the American Mathematical Society

Recommended Citation

Zanello, F. (2015). Zeilberger's KOH theorem and the strict unimodality of q-binomial coefficients. Proceedings of the American Mathematical Society, 143, 2795-2799. http://doi.org/10.1090/S0002-9939-2015-12510-5
Retrieved from: https://digitalcommons.mtu.edu/math-fp/57