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Updated: Jan 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
A positivity conjecture for a quotient of q-binomial coefficients
M Gatzweiler1, C Krattenthaler1
1Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
None:
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.
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