Counting Mal'tsev Clones on Small Sets

Abstract

Idziak (Int. J. Algebra Comput. 9 (1999) 213) has shown that there are only 14 Mal'tsev polynomial clones on a 3 element set and constructed infinitely many such clones on a 4 element set. Here we improve this result by showing that there are, in fact, only countably many Mal'tsev polynomial clones on a 4 element set. A description of all such clones is included. © 2003 Elsevier Science B.V. All rights reserved.