Mona Gatzweiler and Christian Krattenthaler

A positivity conjecture for a quotient of $q$-binomial coefficients

(10 pages)

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. As a corollary 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.


The following versions are available:


Back to Christian Krattenthaler's home page.