Neighborly partitions and the numerators of Rogers–Ramanujan identities-Reference-Cited by-同舟云学术

Neighborly partitions and the numerators of Rogers–Ramanujan identities

Published:2022-10-20 Issue:04 Volume:19 Page:859-872
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Mohsen Zahraa¹²,Mourtada Hussein¹²^ORCID

Affiliation:

1. Université Paris Cité, Sorbonne Université, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris 75013, France

2. Lebanese University, Faculty of Sciences, Department of Mathematics, KALMA Laboratory, Rafik Hariri University Campus, Beirut, Hadath 1533, Lebanon

Abstract

We prove two partition identities which are dual to the Rogers–Ramanujan identities. These identities are inspired by (and proved using) a correspondence between three kinds of objects: a new type of partitions (neighborly partitions), monomial ideals and some infinite graphs.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042123500434

Reference20 articles.

1. Encyclopedia of Mathematics and Its Applications;Andrews G. E.,1976

2. Number Theory in the Spirit of Ramanujan

3. Looking for a New Version of Gordon’s Identities

4. Even–odd partition identities of Rogers–Ramanujan type

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