Presentations for semigroups of full-domain partitions
Abstract
The full-domain partition monoid [Formula: see text] has been discovered independently in two recent studies on connections between diagram monoids and category theory. It is a right restriction Ehresmann monoid, and contains both the full transformation monoid and the join semilattice of equivalence relations. In this paper we give presentations (by generators and relations) for [Formula: see text], its singular ideal and its planar submonoid. The latter is not an Ehresmann submonoid, but it is a so-called grrac monoid in the terminology of Branco, Gomes and Gould. In particular, its structure is determined in part by a right regular band in one-one correspondence with planar equivalences.
Fields of Study & Subjects
semigroups and automata theory
Advanced Algebra and Logic
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- International Journal of Algebra and Computation
- Volume
- 36
- Issue
- 05
- Pages
- 531–579
- Publication date
- 27 February 2026
- Language
- EN