N-graphs,Modular Sidon and Sum-Free Sets,and Partition Identities |
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Authors: | Nathanson Melvyn B |
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Institution: | (1) Department of Mathematics, Lehman College (CUNY), Bronx, New York, 10468 |
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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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Keywords: | partition identities Ferrers graphs modular graphs and N-graphs of partitions Sidon sets sum-free sets additive and combinatorial number theory |
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