A new property of partitions with applications to the Rogers-Ramanujan identities

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Abstract

The order of a partition π (relative to N) is defined as the largest i for which the number of summands in the closed interval [i, i + N - 1] is at least i. By studying the generating function for partitions into distinct parts not exceeding 2N with given order, we are able to derive an identity of importance in the theory of partitions.

Original languageEnglish (US)
Pages (from-to)266-270
Number of pages5
JournalJournal of Combinatorial Theory, Series A
Volume10
Issue number3
DOIs
StatePublished - May 1971

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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