Work

A positivity conjecture for a quotient of q-binomial coefficients

Year: 2025

Type: article

Abstract: We conjecture that, if the quotient of two q -binomial coefficients with the same top argument is a polynomial, then it has non-negative coefficients. We summarise what is known about the conjecture and prove it in two non-trivial cases. Moreover, we move ahead to extend our conjecture to D. Stanton’s fake Gaussian sequences. As a corollary of one of our results we obtain that a polynomial that is conjectured to be a cyclic sieving polynomial for Kreweras words [S. Hopkins and M. Rubey, Selecta Math. (N.S.) 28 (2022), Paper No. 10] is indeed a polynomial with non-negative integer coefficients.

Source: The Ramanujan Journal

DOI: 10.1007/s11139-025-01285-2

Authors: M. Gatzweiler, C. Krattenthaler

Institution: University of Vienna

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Johns Hopkins University, Austrian Science Fund, Universität Wien