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It was added at https://en.wikipedia.org/w/index.php?diff=438062307 that the monoid being "non-commutative and idempotent" implies permutation. I think the property as described cannot mean "free and idempotent", as [a, b, a] wouldn't be called a permutation. Is there a way to clarify the property to really give permutations? Otherwise, is it even meaningful to name the collection type arising from free and idempotent monoid? [[User:J824h|Junghyeon Park]] ([[User talk:J824h|talk]]) 04:27, 11 December 2023 (UTC)
:@[[User:J824h|J824h]]: Sorry it's almost a year later, but that was a really good catch. I reorganized that section into the table a few years back but didn't bother to think through the content enough.
:If you have idempotence but no commutativity to allow reduction, then I'd guess you have the most free regular language ''with no immediate repetitions'' over a given alphabet (of size ''N''). Which itself is isomorphic to the maximal, loop-free, digraph with ''N'' vertices (interpreted as a finite state machine over the alphabet)? Anyways, even if that's interesting, it doesn't strike me as particularly noteworthy or relevant to the article.
:I feel like the ability to generate permutations from a monoid is noteworthy though so I corrected the line. To distinguish from the free monoid, it explicitly says "[[partial permutation]]" now. And maybe it's a bit of hand-waving, but now it just describes the monoid as "non-commutative without repetition". Does that sound good? -- [[User:Zar2gar1|Zar2gar1]] ([[User talk:Zar2gar1|talk]]) 17:37, 21 November 2024 (UTC)
== Rust example ==
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