Dedekind's numbers characterize distributive lattices
The main result is as follows. Let D(n) denote the cardinality of the free bounded distributive lattice on n free generators. A nontrivial algebra is equivalent to a distributive lattice if and only if the number of n-ary polynomials over the algebra is equal to D(n)-2, for all \(n\geq 0.\) The representability rank and the code of the variety of distributive lattices are presented.
code of the variety of distributive lattices
scientific article; zbMATH DE number 4191758