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Questions related to permutations, bijections from a finite (or sometimes infinite) set to itself.

1 vote
0 answers
107 views

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 $[n]$. …
George K's user avatar
  • 422
1 vote
0 answers
93 views

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 $s=(x_1,...,x_n)$ …
George K's user avatar
  • 422