## Bjarni Jens Kristinsson and Henning Úlfarsson (04/06/15)

Benedikt Magnússon, June 1, 2015

Math Colloquium

### Speaker: Bjarni Jens Kristinsson, University of Iceland, and Henning Úlfarsson, Reykjavik University Title: Occurrence graphs of patterns in permutations

Location: Naustið, Endurmenntun (here)
Time: Thursday, June 04, at 15:00-16:00.

### Abstract:

This paper is based on a generalisation of the idea behind the proof of the Simultaneous Shading Lemma by Claesson et al. (2014). We define the occurrence graph $$G_p(\pi)$$ of a pattern $$p$$ in a permutation $$\pi$$ as the graph with the occurrences of $$p$$ in $$\pi$$ as vertices and edges between the vertices if the occurrences differ by exactly one element. We study the general properties of the occurrence graphs and some interesting extreme cases. The main theorem in this paper is that every hereditary property of graphs produces a permutation class.