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Results tagged with co.combinatorics
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user 159356
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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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
Consider a partition $f:S_n\rightarrow [n]$ of $S_n$ into $n$ parts. 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 …
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