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arXiv · 2507.05497

Presentations for semigroups of full-domain partitions

Luka Carroll·James East·Matthias Fresacher
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Abstract

The full-domain partition monoid $P_n^{fd}$ 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 $P_n^{fd}$, 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.

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Luka Carroll, James East, Matthias Fresacher. 2025-07-07. Presentations for semigroups of full-domain partitions. https://arxiv.org/abs/2507.05497

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