MIT Combinatorics Seminar
Dual equivalence graphs, ribbon tableaux and Macdonald polynomials
Sami Assaf (UC Berkeley)
Friday, December 1, 2006 4:15 pm Room 2136
ABSTRACT

We introduce a new combinatorial construction, called a dual
equivalence graph, based on Haiman's 1992 discovery of an equivalence
relation on tableaux which is "dual" to jeudetaquin. We define a
generating function on the vertices of such graphs and show that it is
always Schur positive. We outline the construction of a graph on
standard ktuples of young tableaux which we prove is a dual
equivalence graph for k <= 3. This gives a combinatorial
description of the Schur coefficients of the ribbon tableaux
generating functions introduced by Lascoux, Leclerc and
Thibon. Recalling Haglund's monomial expansion for Macdonald
polynomials, we conclude with a combinatorial formula for the Schur
expansion of Macdonald polynomials indexed by a partition with at most
3 columns.


