In this talk I will describe a new approach to the Haglund-Loehr´s bijection zeta, interchanging couples of statistics (area, dinv) and (bounce, area). The key ingredient is the notion of semimodules over the integer semigroup generated by m and n, i.e. the subsets of natural numbers invariant under addition of m and n. This new point of view allowed us to generalize the map zeta to any slope m/n, and to prove bijectivity in a new series of examples (m=kn-1).
CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar
Tuesday, November 20, 2012 - 2:00pm
Mikhail Mazin
SUNY Stonybrook