What question did this study set out to answer?

The paper aims to provide formal presentations for the full-domain partition monoid and its related structures.

Presentations for semigroups of full-domain partitions

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The paper aims to provide formal presentations for the full-domain partition monoid and its related structures.
Founded on previous studies linking diagram monoids with category theory.
Generated presentations through defining generators and relations.
Analyzed the singular ideal and planar submonoid structures.
Demonstrated that the planar submonoid lacks the properties of an Ehresmann submonoid.
Established a connection between its structure and a right regular band.
Provided insights into the correspondence between planar equivalences and monoid structures.

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Presents structures related to full-domain partitions, indicating their complexity and connections.

Carroll et al. (2026) studied this question.

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