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Results tagged with permutations
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user 159356
Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.
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Is there a characterization for the finite sequences of natural numbers which are the shifts...
Given a natural number $k<n$ and a permutation $\sigma\in S_n$, I will call $k$ a shift of $\sigma$ if there is some $m$ with $\sigma(m)-m\equiv k \mod n$. If one is given a sequence $s=(x_1,...,x_n)$ …
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A maximization problem with permutations
Denote the permutations that map $j$ to $k$ by $s(j,k)$. Set $S(f):=\Sigma_{1\leq i,j\leq n}max_{1\leq k\leq n}|f^{-1}(i)\cap s(j,k)|$. … $ and that it is only achieved by partitioning the permutations of $S_n$ either according to where they map $c$, or according to what they map to $c$, where $c$ can be any specific element of $[n]$. …
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