All centralising monoids with majority witnesses on a four-element set

Abstract

We study unary parts of centraliser clones on the set $\{0,1,2,3\}$, so-called centralising monoids. We describe and count all centralising monoids on the set $\{0,1,2,3\}$ having majority operations as witnesses, and we list the inclusion maximal proper submonoids of the full transformation monoid among them. This extends previous work by Goldstern, Machida and Rosenberg.

arXiv comment43 pages, 9 tables, contains additional raw material (e.g. the computed contexts and some source files) in an ancillary files directory; a shorter version of this article will appear in J. Mult.-Valued Logic Soft Comput