The University of Michigan Combinatorics Seminar


Abstract 

The devil's staircase  a continuous function on the unit interval [0,1] which is not constant, yet is locally constant on an open dense set  is the kind of exotic creature a combinatorialist might never expect to encounter in "real life." I'll show how a devil's staircase arises from the innocentlooking combinatorial problem of parallel chipfiring on the complete graph. This staircase helps explain the surprising tendency of parallel chipfiring to find periodic states of small period. If time permits, I'll also discuss a new generalization of a beautiful formula of Knuth, and its relationship to chipfiring on directed graphs. This talk is based on the papers arXiv:0811.2800 and arXiv:0906.2809. 