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Inequalities for cross-unions of collections of finite sets

Leck, Uwe and Roberts, Ian (2014). Inequalities for cross-unions of collections of finite sets. European Journal of Combinatorics,35:392-401.

Document type: Journal Article
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IRMA ID 75039815xPUB542
Title Inequalities for cross-unions of collections of finite sets
Author Leck, Uwe
Roberts, Ian
Journal Name European Journal of Combinatorics
Publication Date 2014
Volume Number 35
ISSN 0195-6698   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-84882621366
Start Page 392
End Page 401
Total Pages 10
Place of Publication United Kingdom
Publisher Academic Press
HERDC Category C1 - Journal Article (DIISR)
Abstract Some inequalities for cross-unions of families of finite sets are proved that are related to the problem of minimizing the union-closure of a uniform family of given size. The cross-union of two families FF and GG of subsets of [n]={1,2,…,n}[n]={1,2,…,n} is the family F∨G={F∪G:F∈F,G∈G}F∨G={F∪G:F∈F,G∈G}. It is shown that |F∨G|/|F|≥|G∨Bn|/2n|F∨G|/|F|≥|G∨Bn|/2n, where BnBn denotes the power set of [n][n]. Besides, the problem of minimizing |F∨G||F∨G| over all union-closed FF and GG generated by a given number rr of singletons and a given number View the MathML sources>(r2) of two-sets, respectively, is solved.
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Created: Wed, 19 Aug 2015, 12:05:09 CST