Advances and Applications in Discrete Mathematics
Volume 13, Issue 2, Pages 143 - 153
(April 2014)
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ENUMERATING LATTICES OF SUBSETS
Donald M. Davis
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Abstract: If are sets such that no one is contained in another, then there is an associated lattice on corresponding to inclusion relations among unions of the sets. Two lattices on are equivalent if there is a permutation of under which they correspond. We show that for and 4, there are 1, 1, 4, and 50 equivalence classes of lattices on 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. |
Keywords and phrases: enumeration, lattice, Stanley-Reisner ring. |
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