TY - JOUR
T1 - On the q-Analogue of Pólya’s Theorem
AU - Bostan, Alin
AU - Yurkevich, Sergey
N1 - Funding Information:
Supported by DeRerumNatura ANR-19-CE40-0018. Supported by DeRerumNatura ANR-19-CE40-0018, the DOC Fellowship (26101) of the Austrian Academy of Sciences ÖAW, and the Austrian Science Fund FWF (P-34765).
Publisher Copyright:
© The authors. Released under the CC BY-ND license (International 4.0).
PY - 2023
Y1 - 2023
N2 - 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 when q is a complex number, the answer is positive if and only if q is a root of unity.
AB - 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 when q is a complex number, the answer is positive if and only if q is a root of unity.
UR - http://www.scopus.com/inward/record.url?scp=85151819539&partnerID=8YFLogxK
U2 - 10.37236/11269
DO - 10.37236/11269
M3 - Article
AN - SCOPUS:85151819539
SN - 1077-8926
VL - 30
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 2
M1 - P2.9
ER -