Combinatorics of Permutations
Journal of Combinatorial Theory Series A
Excluded permutation matrices and the Stanley-Wilf conjecture
Journal of Combinatorial Theory Series A
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Symposium on Theory of Computing Conference 2006
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Limits of dense graph sequences
Journal of Combinatorial Theory Series B
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Property testing and parameter testing for permutations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Limits of permutation sequences
Journal of Combinatorial Theory Series B
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The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence.