Arithmetic properties of summands of partitions II

Cécile Dartyge, András Sárközy

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6 Citations (Scopus)


Let d ∈ ℕ, ≥ 2. We prove that a positive proportion of partitions of an integer n satisfies the following : for all 1 ≤ a < b ≤ d, the number of the parts congruent to a (mod d) is greater than the number of the parts congruent to b (mod d). We also show that for almost all partitions the rate of the number of square free parts is 6/π (1+o(1)) .

Original languageEnglish
Pages (from-to)383-394
Number of pages12
JournalRamanujan Journal
Issue number3
Publication statusPublished - Dec 1 2005



  • Partitions
  • Residue classes

ASJC Scopus subject areas

  • Algebra and Number Theory

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