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Arrow relations on families of finite sets

✍ Scribed by Mika Watanabe

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 856 KB
Volume: 94
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90306-m

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✦ Synopsis

Watanabe, M., Arrow relations on families of finite sets, Discrete Mathematics 94 (1991) 53-64. Let n, m and k be positive integers. Let X be a set of cardinality n, and let 9 be a family of subsets of X. We write (n, m)-, (n -1, mk), when for all 9 with (S( em, there exists an element x of X such that the family {F -{x}: F E 9) has cardinality at least m -k. We show that (n, m)+(n -1, M -4) for all m s [17n/6], (n, m)-+(n -1, nz -5) for all m s [13n/47, and (n, m)+(n -1, m -6) for all ~fl s [7n/21.

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