Combinatorics Seminar: Permutation tableaux and two models in statistical mechanics

Seminar | October 14 | 12:10-1 p.m. | 939 Evans Hall

 Einar Steingrimsson, University of Strathclyde

 Department of Mathematics

Various pattern-avoiding 0/1-fillings of Ferrers diagrams are in bijection with permutations, where several statistics on the permutations translate into statistics on the filled diagrams (or tableaux). Two such bijections from permutations are to the Le-tableaux arising from Postnikov's work on the nonnegative Grassmannian and the EW-tableaux originally defined in Ehrenborg and van Willigenburg's work on Ferrers graphs. These tableaux and permutations are closely connected to the Partially Asymmetric Exclusion Process and the Abelian Sandpile Model, respectively. I will describe the underlying bijections and some of their properties, and show how the "transformation fondamentale" of Foata and Schützenberger translates between the permutations in question, thus providing a surprising connection between these two physics models. This is joint work with Mark Dukes, Thomas Selig and Jason P. Smith.