Topic
Permutation pattern
About: Permutation pattern is a research topic. Over the lifetime, 165 publications have been published within this topic receiving 2401 citations.
Papers published on a yearly basis
Papers
TL;DR: This paper examines the extremal problem of how many 1-entries an n × n 0-1 matrix can have that avoids a certain fixed submatrix P and proves a linear bound for any permutation matrix P.
597 citations
TL;DR: A polynomial time algorithm is given for the decision problem, and the corresponding counting problem, in the case that P is separable—i.e. contains neither the subpattern (3,1, 4,2) nor its reverse, the sub pattern (2,4, 1,3).
230 citations
TL;DR: In this article, a permutation statistic f : G -> C may be represented uniquely as a linear combination of (classical) permutation patterns: f = Sigma(tau) lambda(f) tau)tau.
Abstract: Any permutation statistic f : G -> C may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: f = Sigma(tau)lambda(f)(tau)tau . To provide exp ...
154 citations
TL;DR: A simple linear time algorithm for checking if a given sequence y of length n contains a factor which is order-isomorphic to a given pattern x, which is a subsequence of consecutive symbols of y is presented.
101 citations
TL;DR: In this paper, a detailed study of permutations via their reduced decompositions and the notion of pattern containment is presented, which is used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals.
Abstract: Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a particular poset. Additionally, the combined frameworks yield several new results about the commutation classes of a permutation. In particular, these describe structural aspects of the corresponding graph of the classes and the zonotopal tilings of a polygon defined by Elnitsky that is associated with the permutation.
74 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 8 |
| 2019 | 10 |
| 2018 | 8 |
| 2017 | 15 |
| 2016 | 11 |