On the $q$-analogue of P\'olya's Theorem
Combinatorics
2023-03-31 v2
Abstract
We answer a question posed by Michael Aissen in 1979 about the -analogue of a classical theorem of George P\'olya (1922) on the algebraicity of (generalized) diagonals of bivariate rational power series. In particular, we prove that the answer to Aissen's question, in which he considers as a variable, is negative in general. Moreover, we show that when is a complex number, the answer is positive if and only if is a root of unity.
Cite
@article{arxiv.2109.02406,
title = {On the $q$-analogue of P\'olya's Theorem},
author = {Alin Bostan and Sergey Yurkevich},
journal= {arXiv preprint arXiv:2109.02406},
year = {2023}
}
Comments
To appear in the Electronic Journal of Combinatorics