Eulerian NumbersIra GesselBrandeis University
September 20,

ABSTRACT


This will be an expository talk on the Eulerian numbers, which arise in several contexts in enumerative combinatorics, probability, and algebra. The Eulerian numbers count permutations by descents and also by excedances, they give the volumes of slices of hypercubes, and they are dimensions of certain vector spaces associated with quotients of polynomial rings by symmetric functions. They also appear in the solution of the Smith College diploma problem. I will describe all of these interpretations of Eulerian numbers and prove some of them. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

