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Results tagged with symmetric-groups
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user 65801
The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
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Probability that k randomly drawn permutations can be arranged to compose to the identity
Only a partial answer, which however is too long for a comment: Let $p_{n,k}$ denote the given probability. Then we have
(1) $p_{n,1} = p_{n,2} = \frac{1}{n!}$, $p_{n,3} = \frac{2\cdot n!-p(n)}{(n!)^2 …
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