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All Centralising Monoids with Majority Witnesses on a Four-element Set
Mike Behrisch

Extending previous work by Goldstern, Machida and Rosenberg, we study unary parts of centraliser clones on a four-element set, 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. As it turns out only 147 out of 1 715 monoids have this property.

Keywords: commutation, centraliser clone, bicentrically closed clone, primitive positive clone, centralising monoid, endoprimal monoid, majority operation, formal concept analysis

AMS Subject Classification (2020): 08A35, 08A02 (08A40).

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