## Thomas Selig (12/10/2018)

Math Colloquium

### Speaker: Thomas Selig, University of Iceland

### Title: The Abelian sandpile model on permutation graphs

Location: Naustið (Endurmenntun)

Time: Friday October 12 at 11.40

### Abstract:

A permutation graph is a graph whose edges are given by the inversions of a permutation. The Abelian sandpile model (ASM) is a Markov chain on the set of so-called configurations of a graph. Of particular interest are the recurrent configurations, i.e. those that appear infinitely often in the long-time running of the model. We exhibit a bijection between the set of recurrent configurations for the ASM on permutation graphs and the set of tiered trees, introduced by Duggan et al. This provides a new bijective proof of a famous result linking the level polynomial of the ASM to the ubiquitous Tutte polynomial. We also show a link between the minimal recurrent configurations and the set of complete non-ambiguous binary trees, introduced by Aval et al.