FC-families, and improved bounds for Frankl's Conjecture
| dc.creator | Morris, Robert | |
| dc.date | 2007-02-13 | |
| dc.date.accessioned | 2026-07-07T07:46:39Z | |
| dc.date.available | 2026-07-07T07:46:39Z | |
| dc.description | A family of sets F is said to be union-closed if A \cup B is in F for every A and B in F. Frankl's conjecture states that given any finite union-closed family of sets, not all empty, there exists an element contained in at least half of the sets. Here we prove that the conjecture holds for families containing three 3-subsets of a 5-set, four 3-subsets of a 6-set, or eight 4-subsets of a 6-set, extending work of Poonen and Vaughan. As an application we prove the conjecture in the case that the largest set has at most nine elements, extending a result of Gao and Yu. We also pose several open questions. | |
| dc.description | 19 pgs, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0702348 | |
| dc.identifier | http://arxiv.org/abs/math/0702348 | |
| dc.identifier | European Journal of Combinatorics 27 (2006) 269-282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123896 | |
| dc.subject | Combinatorics | |
| dc.title | FC-families, and improved bounds for Frankl's Conjecture | |
| dc.type | text |