| Up: | Monoids with two generators and one relation |
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This is an enumeration of finitely-presented monoids with two generators and one relation:
⟨a, b | u=v⟩where:
2 ≤ |u| + |v| ≤ 11This enumeration has 5944 instances in total, after filtering out instances that are trivially isomorphic or anti-isomorphic to those that appeared previously, by some combination of permuting generators, and reversing the relation.
You can download a plain text copy of this data set.
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This means no finite complete rewriting system could be found after the maximum number of attempts.
4 total
| Σ | # | Presentation |
|---|---|---|
| 8 | 481 | ⟨a, b | abbaab=ba⟩ |
| 10 | 2051 | ⟨a, b | ababaaab=ba⟩ |
| 10 | 2080 | ⟨a, b | abbabaab=ba⟩ |
| 11 | 5362 | ⟨a, b | abababa=baab⟩ |
| Properties | Unique | Total |
|---|---|---|
| Grp Com Inf | 1 | 68 |
| Can Com Inf | 2 | 10 |
| Grp Inf | 92 | 686 |
| Can Inf | 1274 | 1284 |
| Noc Inf | 3853 | 3892 |
See Morphocompletion.