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Results tagged with semigroups-and-monoids
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user 7092
A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.
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Is there a name for this condition on a monoid?
Suppose we have a commutative monoid ${\mathcal M}=\langle M,\otimes\rangle$ such that the usual divisibility relation $\leq_\otimes$ given by $a\leq_\otimes b\Leftrightarrow \exists c(a\otimes c=b)$ …
- 5,429
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Accepted
Growth zeta-functions of regular languages
Yes (though the standard term for these is generating functions rather than zeta functions); in fact, there's a relatively straightforward explicit construction for finding the generating function for …
- 1,951