### Abstract

Let n = n_{1} + n_{2} + ⋯ + n_{j} a partition Π of n. One will say that this partition represents the integer a if there exists a subsum n_{i1}, + n_{i2} + ⋯ + n_{il} 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 language | French |
---|---|

Pages (from-to) | 27-48 |

Number of pages | 22 |

Journal | Discrete Mathematics |

Volume | 200 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Apr 6 1999 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## Cite this

*Discrete Mathematics*,

*200*(1-3), 27-48. https://doi.org/10.1016/S0012-365X(98)00330-6