Signed Partitions and Rogers-Ramanujan type Identities

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Hauptverfasser: Alanazi, Abdulaziz M., Munagi, Augustine O., Sills, Andrew V.
Format: Preprint
Veröffentlicht: 2025
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author Alanazi, Abdulaziz M.
Munagi, Augustine O.
Sills, Andrew V.
author_facet Alanazi, Abdulaziz M.
Munagi, Augustine O.
Sills, Andrew V.
contents 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 Göllnitz--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 Göllnitz--Gordon identities, different from that of Andrews. Both analytic and bijective proofs are presented.
format Preprint
id arxiv_https___arxiv_org_abs_2505_08099
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Signed Partitions and Rogers-Ramanujan type Identities
Alanazi, Abdulaziz M.
Munagi, Augustine O.
Sills, Andrew V.
Combinatorics
Number Theory
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 Göllnitz--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 Göllnitz--Gordon identities, different from that of Andrews. Both analytic and bijective proofs are presented.
title Signed Partitions and Rogers-Ramanujan type Identities
topic Combinatorics
Number Theory
url https://arxiv.org/abs/2505.08099