Arithmetic properties of summands of partitions II

Cécile Dartyge, András Sárközy

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume10
Issue number3
DOIs
Publication statusPublished - Dec 1 2005

    Fingerprint

Keywords

  • Partitions
  • Residue classes

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this