1 research outputs found
On centralizers of finite lattices and semilattices
We study centralizer clones of finite lattices and semilattices. For
semilattices, we give two characterizations of the centralizer and also derive
formulas for the number of operations of a given essential arity in the
centralizer. We also characterize operations in the centralizer clone of a
distributive lattice, and we prove that the essential arity of operations in
the centralizer is bounded for every finite (possibly nondistributive) lattice.
Using these results, we present a simple derivation for the centralizers of
clones of Boolean functions.Comment: 21 pages, 4 figure