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A survey of consecutive patterns in permutations

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Recent Trends in Combinatorics

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 159))

Abstract

A consecutive pattern in a permutation π is another permutation \(\sigma\) determined by the relative order of a subsequence of contiguous entries of π. Traditional notions such as descents, runs, and peaks can be viewed as particular examples of consecutive patterns in permutations, but the systematic study of these patterns has flourished in the last 15 years, during which a variety of different techniques have been used. We survey some interesting developments in the subject, focusing on exact and asymptotic enumeration results, the classification of consecutive patterns into equivalence classes, and their applications to the study of one-dimensional dynamical systems.

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Acknowledgements

Partially supported by grant #280575 from the Simons Foundation and by grant H98230-14-1-0125 from the NSA.

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Authors and Affiliations

  1. Department of Mathematics, Dartmouth College, Hanover, NH, 03755, USA

    Sergi Elizalde

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  1. Sergi Elizalde
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Correspondence to Sergi Elizalde .

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Editors and Affiliations

  1. Dept of Math, Statistics & Comp.Sc, Macalester College, St. Paul, Minnesota, USA

    Andrew Beveridge

  2. Dept. of Mathematics, University of South Carolina, Columbia, South Carolina, USA

    Jerrold R. Griggs

  3. Dept. of Mathematics, Iowa State University, Ames, Iowa, USA

    Leslie Hogben

  4. School of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA

    Gregg Musiker

  5. School of Mathematics & Computer Sc, Georgia Institute of Technology, Atlanta, Georgia, USA

    Prasad Tetali

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Elizalde, S. (2016). A survey of consecutive patterns in permutations. In: Beveridge, A., Griggs, J., Hogben, L., Musiker, G., Tetali, P. (eds) Recent Trends in Combinatorics. The IMA Volumes in Mathematics and its Applications, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-319-24298-9_24

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