Optimizing diversity
| dc.creator | Frein, Yannick | |
| dc.creator | Lévêque, Benjamin | |
| dc.creator | Sebo, Andras | |
| dc.date | 2007-11-19 | |
| dc.date.accessioned | 2026-07-07T08:43:48Z | |
| dc.date.available | 2026-07-07T08:43:48Z | |
| dc.description | We consider the problem of minimizing the size of a family of sets G such that every subset of 1,...,n can be written as a disjoint union of at most k members of G, where k and n are given numbers. This problem originates in a real-world application aiming at the diversity of industrial production. At the same time, the minimum of G so that every subset of 1,...,n is the union of two sets in G has been asked by Erdos and studied recently by Furedi and Katona without requiring the disjointness of the sets. A simple construction providing a feasible solution is conjectured to be optimal for this problem for all values of n and k and regardless of the disjointness requirement; we prove this conjecture in special cases including all (n,k) for which n <= 3k holds, and some individual values of n and k. | |
| dc.identifier | https://arxiv.org/abs/0711.2998 | |
| dc.identifier | http://arxiv.org/abs/0711.2998 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142443 | |
| dc.subject | Discrete Mathematics | |
| dc.title | Optimizing diversity | |
| dc.type | text |