The number of equationally additive clones on finite sets

Behrisch, Mike; Aichinger, Erhard; Rossi, Berna

doi:10.34726/3067

Record link:

http://hdl.handle.net/20.500.12708/136147
https://doi.org/10.34726/3067

Title:

The number of equationally additive clones on finite sets

Citation:

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

reposiTUm DOI:

10.34726/3067

Publication Type:

Presentation - Conference Presentation

Vortrag - Conference Presentation

Language:

English

Authors:

Behrisch, Mike
Aichinger, Erhard
Rossi, Berna

Organisational Unit:

E104-01 - Forschungsbereich Algebra

Date (published):

29-Aug-2022

Event name:

Summer School on General Algebra and Ordered Sets 2022

Event date:

28-Aug-2022 - 2-Sep-2022

Event place:

Hotel Sorea Titris, Tatranská Lomnica, Vysoké Tatry, Slovakia

Keywords:

clone; constantive clone; equationally additive; algebraic set

Abstract:

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.

Project (external):

Austrian Science Fund (FWF)

Project ID:

P 33878

Research Areas:

Fundamental Mathematics Research: 100%

Science Branch:

1010 - Mathematik: 100%

License:

CC BY-NC-SA 4.0