Behrisch, M., Aichinger, E., & Rossi, B. (2022, August 29). The number of equationally additive clones on finite sets [Conference Presentation]. Summer School on General Algebra and Ordered Sets 2022, Hotel Sorea Titris, Tatranská Lomnica, Vysoké Tatry, Slovakia. https://doi.org/10.34726/3067
Summer School on General Algebra and Ordered Sets 2022
28-Aug-2022 - 2-Sep-2022
Hotel Sorea Titris, Tatranská Lomnica, Vysoké Tatry, Slovakia
clone; constantive clone; equationally additive; algebraic set
For a clone on a finite set, a finitary relation is algebraic if it can be described as solution set of a finite system of equations using only functions from that clone. We call a clone equationally additive if the union of any two algebraic relations of the same arity is again algebraic. In the talk we shall report on how many equationally additive clones (and clones with constants) there are on carrier sets of size 2, 3 and beyond.