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.
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References
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Nathanson, M.B. N-graphs, Modular Sidon and Sum-Free Sets, and Partition Identities. The Ramanujan Journal 4, 59–67 (2000). https://doi.org/10.1023/A:1009830023023
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DOI: https://doi.org/10.1023/A:1009830023023