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On the f-vectors of Cutsets in the Boolean Lattice

✍ Scribed by Matthew Haines; Shahriar Shahriari

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
102 KB
Volume
93
Category
Article
ISSN
0097-3165

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✦ Synopsis

A cutset in the poset 2 [n] , of subsets of [1, ..., n] ordered by inclusion, is a subset of 2 [n] that intersects every maximal chain. Let 0 : 1 be a real number. Is it possible to find a cutset in 2 [n] that, for each 0 i n, contains at most : ( n i ) subsets of size i ? Let :(n) be the greatest lower bound of all real numbers for which the answer is positive. In this note we prove the rather surprising fact that lim n Γ„ :(n)=0.

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