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.