Year: 2025
Type: preprint
Abstract: In this paper, we present a new Rogers--Ramanujan type identity for overpartitions by extending the asymmetrical version of Schur's theorem due to Lovejoy to a broader class of infinite products. More precisely, we provide a combinatorial interpretation of the following product, for any positive integer $k$, as a generating function for a class of overpartitions in which parts appear in $2^k - 1$ colors: \[ \frac{(-y_1 q;q)_\infty \cdots (-y_k q;q)_\infty}{(y_1 d q;q)_\infty}. \] Our proof is bijective and unifies two earlier approaches: Lovejoy's bijective proof of the asymmetrical Schur theorem and the iterative-bijective technique developed by Corteel and Lovejoy.
Source: arXiv (Cornell University)
Author: Velenik, Laure
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Université de Genève
OpenAlex ID: W4414809382
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