Abstract

The paper is concerned with the problem of computing the number of elements of a free distributive lattice, and with related problems. A recursive formula, using the order of a free distributive lattice with one less generators, is obtained to compute the number of elements of any principal filter of the lattice, in particular the lattice itself. Recursive formulas for the fixed points of the antiorder isomorphism lead easily to the fact that when the number of generators is even the number of elements of the lattice is even. For basic properties of free distributive lattices we refer the reader to [1].

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