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On Union-Closed Families, I

✍ Scribed by Robert T. Johnson; Theresa P. Vaughan

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 93 KB
Volume: 85
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2899

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📜 SIMILAR VOLUMES

✍ Robert T. Johnson; Theresa P. Vaughan 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 174 KB

A union closed family A is a finite family of sets such that the union of any two sets in A is also in A. The conjecture under consideration is Conjecture 1: For every union closed family A, there exists some x contained in at least half the members of A. We study the structure of such families (as

Density of union-closed families

✍ Piotr Wójcik 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 425 KB

W6jcik, P., Density of union-closed families, Discrete Mathematics 105 (1992) 259-267. Two theorems related to Frankl's conjecture about union-closed families are proved. The first one states how small the sum of degrees in an m-element set may be. Our second result deals with the smallest densities

Union-closed families of sets

✍ Piotr Wójcik 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 532 KB

We use a lower bound on the number of small sets in an idea1 to show that for each unionclosed family of n sets there exists an element which belongs to at least of them, provided n is large enough.

Remarks on nonmeasurable unions of big p

Remarks on nonmeasurable unions of big point families

✍ Robert Rałowski 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB

## Abstract We show that under some conditions on a family __A__ ⊂ __I__ there exists a subfamily __A__~0~ ⊂ __A__ such that ∪ __A__~0~ is nonmeasurable with respect to a fixed ideal __I__ with Borel base of a fixed uncountable Polish space. Our result applies to the classical ideal of null subsets

Largest size and union of Helly families

✍ Zsolt Tuza 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 557 KB

Closing in on a “familial cholestasis ge

Closing in on a “familial cholestasis gene”

✍ Joseph Wagstaff; Maureen M. Jonas 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 430 KB