Year: 2025
Type: preprint
Abstract: We construct a $k$-fold $q$-series as a generating function of $k$-regular partitions for each positive integer $k$. The $k=1$ case is one of Euler's $q$-series identities pertaining to the partitions into distinct parts. The construction is combinatorial. Although we find a connection to Bessel polynomials in the $k=2$ case, this note is certainly not a study of Bessel polynomials and their $q$-analogs.
Source: arXiv (Cornell University)
Author: Kurşungöz, Kağan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414848301
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