The number of smallest parts in the partitions of n

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Abstract

We denote by spt(n) the total number of appearances of the smallest part in each integer partition of n. We shall relate spt(n) to the Atkin-Garvan moments of ranks, and we shall prove that 5 | spt(5n + 4), 7 | spt(7n + 5) and 13 | spt(13n + 6).

Original languageEnglish (US)
Pages (from-to)133-142
Number of pages10
JournalJournal fur die Reine und Angewandte Mathematik
Issue number624
DOIs
StatePublished - Nov 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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