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arXiv · 1311.6664

Enumerating lattices of subsets

Donald M. Davis
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Abstract

Given k sets such that no one is contained in another, there is an associated lattice on the power set P([k]) corresponding to inclusion relations among unions of the sets. Two lattices on P([k]) are equivalent if there is a permutation of [k] under which they correspond. We show that for k=1, 2, 3, and 4, there are 1, 1, 4, and 50 equivalence classes of lattices on P([k]) obtained from sets in this way. We cannot find a reference to previous work on this enumeration problem in the literature, and so wish to introduce it for subsequent investigation. We explain how the problem arose from algebraic topology.

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Donald M. Davis. 2013-12-10. Enumerating lattices of subsets. https://arxiv.org/abs/1311.6664

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