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Mathematics > Combinatorics

arXiv:math/0405266 (math)
[Submitted on 14 May 2004 (v1), last revised 28 Feb 2006 (this version, v2)]

Title:A Permutation Regularity Lemma

Authors:Joshua N. Cooper
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Abstract: We introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences. This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that permutations which scatter small intervals contain all possible patterns of a given size, a proof that every permutation avoiding a specified pattern has a nearly monotone linear-sized subset, and a ``thin deletion'' result. We also show how one can count sub-patterns of a permutation with an integral, and relate our results to permutation quasirandomness in a manner analogous to the graph-theoretic setting.
Comments: Minor corrections, to appear in Electronic Journal of Combinatorics
Subjects: Combinatorics (math.CO)
MSC classes: 05D99
Cite as: arXiv:math/0405266 [math.CO]
  (or arXiv:math/0405266v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.math/0405266

Submission history

From: Joshua N. Cooper [view email]
[v1] Fri, 14 May 2004 03:23:49 UTC (18 KB)
[v2] Tue, 28 Feb 2006 21:44:09 UTC (18 KB)
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