Growth and identities of monogenic free adequate monoids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916946661867520 |
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| author | Aird, Thomas Heath, Daniel |
| author_facet | Aird, Thomas Heath, Daniel |
| contents | Motivated by recent advances in inverse semigroup theory, we investigate the growth of and identities satisfied by free left and free two-sided adequate monoids. We explicitly compute the growth of the monogenic free left adequate monoid with the usual unary monoid generating set and show it has intermediate growth owing to a connection with integer partitions. In the two-sided case, we establish a lower bound on the (idempotent) growth rate of the monogenic free adequate monoid, showing that it grows exponentially. We completely classify the enriched identities satisfied by the monogenic free left adequate monoid and deduce that it satisfies the same monoid identities as the sylvester monoid. In contrast, we show that the monogenic free two-sided adequate monoid satisfies no non-trivial monoid identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growth and identities of monogenic free adequate monoids Aird, Thomas Heath, Daniel Rings and Algebras Combinatorics Group Theory 20M05 (Primary), 08B20, 20M07, 05C05 Motivated by recent advances in inverse semigroup theory, we investigate the growth of and identities satisfied by free left and free two-sided adequate monoids. We explicitly compute the growth of the monogenic free left adequate monoid with the usual unary monoid generating set and show it has intermediate growth owing to a connection with integer partitions. In the two-sided case, we establish a lower bound on the (idempotent) growth rate of the monogenic free adequate monoid, showing that it grows exponentially. We completely classify the enriched identities satisfied by the monogenic free left adequate monoid and deduce that it satisfies the same monoid identities as the sylvester monoid. In contrast, we show that the monogenic free two-sided adequate monoid satisfies no non-trivial monoid identities. |
| title | Growth and identities of monogenic free adequate monoids |
| topic | Rings and Algebras Combinatorics Group Theory 20M05 (Primary), 08B20, 20M07, 05C05 |
| url | https://arxiv.org/abs/2509.09543 |