## Involve: A Journal of Mathematics

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

### Occurrence graphs of patterns in permutations

Bjarni Jens Kristinsson and Henning Ulfarsson

#### Abstract

We define the occurrence graph ${G}_{p}\left(\pi \right)$ of a pattern $p$ in a permutation $\pi $ as the graph whose vertices are the occurrences of $p$ in $\pi $, 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**

Received: 11 July 2016

Revised: 15 February 2019

Accepted: 18 February 2019

First available in Project Euclid: 13 August 2019

**Permanent link to this document**

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

**Subjects**

Primary: 05A05: Permutations, words, matrices 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05C30: Enumeration in graph theory

**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