| author: | Dan Romik |
|---|---|
| title: | Permutations with short monotone subsequences |
| keywords: | Robinson-Schensted correspondence, Erdős-Szekeres theorem, limit shape |
| abstract: |
We consider permutations of
1,2,...,n
whose longest monotone subsequence is of length
2
n
and are therefore extremal for the
Erdős-Szekeres Theorem. Such permutations
correspond via the Robinson-Schensted correspondence to
pairs of square
n× n
Young tableaux. We show that all the bumping
sequences are constant and therefore these permutations
have a simple description in terms of the pair of square
tableaux. We deduce a limit shape result for the plot of
values of the typical such permutation, which in particular
implies that the first value taken by such a permutation is
with high probability
(1+o(1))n
.
2
/2
|
| If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |
| reference: | Dan Romik (2005), Permutations with short monotone subsequences, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 57-62 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dmAE0112.ps.gz (269 K) |
| ps-source: | dmAE0112.ps (4029 K) |
| pdf-source: | dmAE0112.pdf (433 K) |
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