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- W2072589849 abstract "Let S(n) denote the set of subsets of an n-element set. For an element x of S(n), let Γx and Px denote, respectively, all (|x| −1)-element subsets of x and all (|x| + 1)-element supersets of x in S(n). Several inequalities involving Γ and P are given. As an application, an algorithm for finding an x-element antichain X∗ in S(n) satisfying | YX∗ | ⩽ | YX | for all x-element antichains X in S(n) is developed, where YX is the set of all elements of S(n) contained in an element of X. This extends a result of Kleitman [9] who solved the problem in case x is a binomial coefficient." @default.
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- W2072589849 date "1974-09-01" @default.
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- W2072589849 title "Inequalities concerning numbers of subsets of a finite set" @default.
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- W2072589849 doi "https://doi.org/10.1016/0097-3165(74)90010-7" @default.
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