#semigroup — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #semigroup, aggregated by home.social.
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Here's a weirdo semigroup:
0 1 2 3 4 5
0| 5 5 5 2 0 3
1| 5 5 5 2 2 3
2| 5 5 5 2 2 3
3| 2 2 2 3 3 5
4| 2 1 2 3 4 5
5| 3 3 3 5 5 2Besides associativity, it has the properties that:
* There is no left-identity or right-identity
* Neither a*_ nor _*a is ever a constant function (i.e., no row nor column is constant)
* The operator is surjective (no element fails to appear in the table)I wrote a constraint solver to find such semigroups, and the curious thing is that if we want to limit the number of entries where a*a = a, then it appears that n-2 such constraints are satisfiable, but n-1 of them are not.
Relevance: https://blog.computationalcomplexity.org/2025/04/i-want-applicaion-of-this-application.html where there is a proof that at least one element must satisfy a*a = a, but Bill Gasarch asks for a "non-obvious" finite example. Is it true that all non-obvious examples must have _two_ such elements?
I realized about halfway through that this is probably the wrong way to go about it -- it would be better to generate rules instead of tables, and test those rules for associativity and non-obviousness. Then we could find if there's some "compactly described" semigroup with the desired properties.
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🚀 just uploaded to https://fpilluminated.com
Folding Cheat Sheet #8 - Folding with Monoids.
39 slides - Twelve examples.
Direct link: https://fpilluminated.com/deck/240
#haskell #scala #monoid #semigroup #fold #foldMap #combineAll #cats #fp #functional_programming
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The more I learn about quasigroups, the more I think they deserve the name in a way that semigroups don't.
Semigroups that faithfully embed into a group maybe are ok b/c they're "half the group" (e.g. positive reals inside the reals, under addition).
But not general semigroups. They need a new name.
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We just received another publication from 2 other Ukrainian Research Fellows in the research area #algebra. 🔣 Click at the link below!
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