Antichains in the set of subsets of a multiset |
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Authors: | G.F Clements |
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Affiliation: | University of Colorado, Boulder, CO 80309, USA |
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Abstract: | A set F of distinct subsets x of a finite multiset M (that is, a set with several different kinds of elements) is a c-antichain if for no c + 1 elements x0, x1, …, xc of F does x0 ? x1 ? ··· ? xc hold. The weight of F, wF, is the total number of elements of M in the various elements x of F. For given integers f and c, we find min wF, where the minimum is taken over all f-element c-antichains F. Daykin [9, 10] has solved this problem for ordinary sets and Clements [3] has solved it for multisets, but only for c = 1. |
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