An Asymptotic Version of a Theorem of Knuth

Details An Asymptotic Version of a Theorem of Knuth An Asymptotic Version of a Theorem of Knuth

2009-06-28

arxiv.org/abs/0906.5167v2

Mathematics

Combinatorics

9 pages

Scientific paper

Let $S(d,N)$ denote the number of permutations in the symmetric group on
$[N]$ which have no decreasing subsequence of length $d+1.$ We prove that
$S(d,dn)$ is asymptotically equal to the number of standard Young tableaux of
rectangular shape $R(d,2n)$ in the limit $n \to \infty,$ with $d$ fixed.

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