We answer a question posed by Michael Aissen in 1979 about the $q$-analogue of a classical theorem of George Pólya (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 $q$ as a variable, is negative in general. Moreover, we show that the answer is positive if and only if $q$ is a root of unity.
@article{10_37236_11269,
author = {Alin Bostan and Sergey Yurkevich},
title = {On the \(q\)-analogue of {P\'olya's} theorem},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11269},
zbl = {1512.05055},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11269/}
}
TY - JOUR
AU - Alin Bostan
AU - Sergey Yurkevich
TI - On the \(q\)-analogue of Pólya's theorem
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11269/
DO - 10.37236/11269
ID - 10_37236_11269
ER -
%0 Journal Article
%A Alin Bostan
%A Sergey Yurkevich
%T On the \(q\)-analogue of Pólya's theorem
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11269/
%R 10.37236/11269
%F 10_37236_11269
Alin Bostan; Sergey Yurkevich. On the \(q\)-analogue of Pólya's theorem. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11269
