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Results tagged with semigroups-and-monoids
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user 45255
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.
2
votes
Coin problem with permutations
I guess the answer should be that $(a,b,c)$ fills the line if and only if there is an integral combination of its permutations equaling $(1,1,1)$. We want the elementary divisors of a certain $3 \tim …
13
votes
1
answer
2k
views
Coin problem with permutations
Let $a,b,c$ be positive integers with gcd$(a,b,c)=1$, and let $\mathbb{N}$ denote the set of nonnegative integers.
It is well known that $\mathbb{N} \setminus (a \mathbb{N}+b \mathbb{N} + c \mathbb{N …
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