On the Height of the Poset of Endomorphism Monoids of Regular Relations
Maja Pech and Dragan Maulovic
The regular relations form one of the more intriguing classes of relations that are used to describe maximal clones in the Rosenberg’s characterization theorem. In this paper we study the partially ordered set of endomorphism monoids of regular relations and show that it contains long chains. We show that the length of maximal chains in this poset is bounded from below by O(√n) and from above by n-2, where n is the number of elements of the underlying set.