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

11 votes

Number of permutations with longest increasing subsequences of length at most $n$

The gross asymptotics are that the $k$th root of the number of such permutations approaches $n^2$. … Note that in most of the literature, $k$ and $n$ will play the opposite roles, i.e., the question will be about enumeration of permutations in $S_n$ with no increasing subsequence of size greater than …
Michael Albert's user avatar