Abstract
A set X of subsets of an n-element set S is called an anti-chain if no two elements of X are related by set-wise inclusion. Sperner showed [8] that max |X|=( n [ n 2 ] ) , where | X| denotes the number of elements in X and the maximum is taken over all anti-chains of subsets of S. Let non-negative integers i o < n and m i o ≠0, m i o +1,… m n be given. In this paper we give an algorithm for calculating max | X| where the maximum is taken only over anti-chains containing exactly m i i-element subsets of S for i o ⩽ i ⩽ n.
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