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 less than or equal to i less than or equal to n, contains at most alpha((n)(1)) subsets possible to find a cutset in 2([n]) that, for each 0 less than or equal to i less than or equal to n, contains at most alpha((n)(1))subsets of size i? Let alpha (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--> s) alpha (n) = 0. (C) 2001 Academic Press. [References: 13]
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