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

6 votes
Accepted

Betweenness in permutations

By induction, for any $k$ permutations, there is a subset $S_k \subseteq \{1,2,\dots,n\}$ of size at least $n^{1/2^{k-1}}$ that is monotone in each of the $k$ permutations, and so the relations $R(\pi_ … A construction of $k$ permutations of length $2^{2^{k-1}}$ with no common monotone subsequence of length $3$ does not seem to be easy to describe. …
Jan Kyncl's user avatar
  • 6,101
7 votes

Is there an efficient algorithm to check whether two matrices are the same up to row and col...

Regarding the first question: there is a counterexample of size $91$. There are four non-isomorphic finite projective planes of order $9$: https://doi.org/10.1016/0012-365X(91)90280-F, http://oeis.or …
Jan Kyncl's user avatar
  • 6,101