Year: 2026
Type: preprint
Abstract: In this paper, we revisit the work of Berkovich and Paule on variants of the Andrews-Gordon identities. We find a generalization of their principal polynomial identity and, as a consequence, obtain new $\vec M$ versions of the Andrews-Gordon identities. More precisely, for non-negative integers $M_1\ge M_2\ge M_3\ge\ldots\ge M_ν$, we show that a broad class of multi-sums of the form $$ \sum\limits_{\mathbf n} \frac{ q^{ N_1^2+\cdots+N_ν^2 - M_1N_1 - M_2N_2 - \cdots - M_νN_ν} }{ (q)_{n_1}(q)_{n_2}\cdots(q)_{n_ν} } $$ can be expressed as a sum of products. Above, we use standard notations for $q$-Pochhammer symbols and $N_i = \sum\limits_{k=i}^νn_k$ for $1\le i\le ν$.
Source: arXiv (Cornell University)
Authors: Berkovich, Alexander, Dhar, Aritram
Institution: University of Florida
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212053915