Presentations for semigroups of full-domain partitions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909678853685248 |
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| author | Carroll, Luka East, James Fresacher, Matthias |
| author_facet | Carroll, Luka East, James Fresacher, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Presentations for semigroups of full-domain partitions Carroll, Luka East, James Fresacher, Matthias Rings and Algebras Group Theory 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. |
| title | Presentations for semigroups of full-domain partitions |
| topic | Rings and Algebras Group Theory |
| url | https://arxiv.org/abs/2507.05497 |