Signed Partitions and Rogers-Ramanujan type Identities
Combinatorics
2025-05-14 v1 Number Theory
Abstract
George Andrews [\emph{Bull. Amer. Math. Soc.}, 2007, 561--573] introduced the idea of a \emph{signed partiton} of an integer; similar to an ordinary integer partitions, but where some of the parts could be negative. Further, Andrews reinterpreted the classical G\"ollnitz--Gordon partition identities in terms of signed partitions. In the present work, we provide interpretations of the sum sides of Rogers--Ramanujan type identities, including a new signed partition interpretation of the G\"ollnitz--Gordon identities, different from that of Andrews. Both analytic and bijective proofs are presented.
Cite
@article{arxiv.2505.08099,
title = {Signed Partitions and Rogers-Ramanujan type Identities},
author = {Abdulaziz M. Alanazi and Augustine O. Munagi and Andrew V. Sills},
journal= {arXiv preprint arXiv:2505.08099},
year = {2025}
}