Centralising monoids with conservative majority operations as witnesses
Mike Behrisch · 2021
We study the commutation condition between unary functions and conservative majority operations on finite sets, that is, centralising monoids with conservative majority operations as witnesses. Focussing on four-element sets, we obtain and count all such monoids and find the maximal ones with respect to set inclusion strictly below the full transformation monoid. We also compare the situation to centralising monoids given by arbitrary majority operations without the conservativeness restriction.