Centralizing Monoids and the Arity of Witnesses

Multi-variable functions defined over a fixed finite set A are considered. A centralizing monoid M is a set of unary functions on A which commute with all members of some set F of functions on A. The set F is called a witness of M. We show that every centralizing monoid has a witness whose arity does not exceed |A|. Next, we present examples of centralizing… CONTINUE READING