## Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 6 (2019), 901-918.

### Occurrence graphs of patterns in permutations

#### Abstract

We define the occurrence graph $Gp(π)$ of a pattern $p$ in a permutation $π$ as the graph whose vertices are the occurrences of $p$ in $π$, with edges between the vertices if the occurrences differ by exactly one element. We then study properties of these graphs. The main theorem in this paper is that every hereditary property of graphs gives rise to a permutation class.

#### Article information

Source
Involve, Volume 12, Number 6 (2019), 901-918.

Dates
Revised: 15 February 2019
Accepted: 18 February 2019
First available in Project Euclid: 13 August 2019

https://projecteuclid.org/euclid.involve/1565661763

Digital Object Identifier
doi:10.2140/involve.2019.12.901

Mathematical Reviews number (MathSciNet)
MR3990788

Zentralblatt MATH identifier
07116060

Keywords
graph permutation subgraph pattern

#### Citation

Kristinsson, Bjarni Jens; Ulfarsson, Henning. Occurrence graphs of patterns in permutations. Involve 12 (2019), no. 6, 901--918. doi:10.2140/involve.2019.12.901. https://projecteuclid.org/euclid.involve/1565661763

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