\(N\)-graphs, modular Sidon and sum-free sets, and partition identities

DOI10.1023/A:1009830023023zbMATH Open1012.11091arXivmath/0002173OpenAlexW1483356989MaRDI QIDQ1567062

Melvyn B. Nathanson

Publication date: 23 June 2003

Published in: The Ramanujan Journal (Search for Journal in Brave)

Abstract: Using a new graphical representation for partitions, the author obtains a family of partition identities associated with partitions into distinct parts of an arithmetic progression, or, more generally, with partitions into distinct parts of a set that is a finite union of arithmetic progressions associated with a modular sum-free Sidon set. Partition identities are also constructed for sets associated with modular sum-free sets.

Full work available at URL: https://arxiv.org/abs/math/0002173

zbMATH Keywords

Sidon setspartition identitiesFerrers graphsmodular graphs\(N\)-graphs of partitionsmodular sum-free setsmodular sum-free Sidon set

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial aspects of representation theory (05E10) Other combinatorial number theory (11B75) Elementary theory of partitions (11P81)

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