The growth of free inverse monoids
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917721688506368 |
|---|---|
| author | Kambites, Mark Nyberg-Brodda, Carl-Fredrik Szakács, Nóra Webb, Richard |
| author_facet | Kambites, Mark Nyberg-Brodda, Carl-Fredrik Szakács, Nóra Webb, Richard |
| contents | We compute the rate of exponential growth of the free inverse monoid of rank $r$ (and hence an upper bound on the corresponding rate for all $r$-generated inverse monoids and semigroups). This turns out to be an algebraic number strictly between the obvious bounds of $2r-1$ and $2r$, tending to $2r$ as the rank tends to infinity. We also find an explicit expression for the exponential growth rate of the number of idempotents, and prove that this tends to $\sqrt{e(2k-1)}$ as $k \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The growth of free inverse monoids Kambites, Mark Nyberg-Brodda, Carl-Fredrik Szakács, Nóra Webb, Richard Group Theory Rings and Algebras 20M18 (primary), 20M05, 05C05 (secondary) We compute the rate of exponential growth of the free inverse monoid of rank $r$ (and hence an upper bound on the corresponding rate for all $r$-generated inverse monoids and semigroups). This turns out to be an algebraic number strictly between the obvious bounds of $2r-1$ and $2r$, tending to $2r$ as the rank tends to infinity. We also find an explicit expression for the exponential growth rate of the number of idempotents, and prove that this tends to $\sqrt{e(2k-1)}$ as $k \to \infty$. |
| title | The growth of free inverse monoids |
| topic | Group Theory Rings and Algebras 20M18 (primary), 20M05, 05C05 (secondary) |
| url | https://arxiv.org/abs/2407.10489 |