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Bounds on Superpatterns Containing all Layered Permutations

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Abstract

In the study of pattern containment, a \(k\)-superpattern is a permutation which contains all \(k!\) permutations of length \(k\) as a pattern. One may also consider restricted superpatterns, i.e. a permutation which contains, as a pattern, every element in some subclass of the set of permutations of length \(k\). Here, we find lower and upper bounds on a superpattern which contains all layered \(k\)-permutations. Also, we exhibit a connection between the sum of depths of null-balanced binary trees on \(k\) vertices, as defined in (Proceedings of American Conference on Applied Mathematics, Cambridge, MA, pp 377–381 2012).

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Daniel Gray

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  1. Daniel Gray
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Correspondence to Daniel Gray.

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Gray, D. Bounds on Superpatterns Containing all Layered Permutations. Graphs and Combinatorics 31, 941–952 (2015). https://doi.org/10.1007/s00373-014-1429-x

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  • DOI: https://doi.org/10.1007/s00373-014-1429-x

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