Sur les ensembles représentés par les partitions d'un entier n

Marc Deléglise, Paul Erdos, Jean Louis Nicolas

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let n = n1 + n2 + ⋯ + nj a partition Π of n. One will say that this partition represents the integer a if there exists a subsum ni1, + ni2 + ⋯ + nil equal to a. The set ℰ(Π) is defined as the set of all integers a represented by Π. Let Script A sign be a subset of the set of positive integers. We denote by p(Script a sign, n) the number of partitions of n with parts in Script a sign, and by p(Script a sign, n) the number of distinct sets represented by these partitions. Various estimates for p̂(Script a sign, n) are given. Two cases are more specially studied, when Script a sign is the set {1, 2, 4, 8, 16, . . .} of powers of 2, and when Script a sign is the set of all positive integers. Two partitions of n are said to be equivalent if they represent the same integers. We give some estimations for the minimal number of parts of a partition equivalent to a given partition.

Original languageFrench
Pages (from-to)27-48
Number of pages22
JournalDiscrete Mathematics
Volume200
Issue number1-3
DOIs
Publication statusPublished - Apr 6 1999

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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