An Asymptotic Version of a Theorem of Knuth

Jonathan Novak

An Asymptotic Version of a Theorem of Knuth

Combinatorics 2010-02-12 v2

Authors: Jonathan Novak

Abstract

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.

Keywords

permutations decreasing subsequences standard Young tableaux asymptotic enumeration Knuth theorem

Cite

@article{arxiv.0906.5167,
  title  = {An Asymptotic Version of a Theorem of Knuth},
  author = {Jonathan Novak},
  journal= {arXiv preprint arXiv:0906.5167},
  year   = {2010}
}

Comments

9 pages

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