Learn More
We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of [Schützenberger '77] for standard Young tableaux. We apply this to give a new combinatorial rule for the K-theory Schubert calculus of Grassmannians via K-theoretic jeu de taquin, providing an alternative to the rules of [Buch '02] and others. This rule naturally(More)
In this paper, starting with a simply laced root system, we define a tri-angulated category which we call the m-cluster category, and we show that it encodes the combinatorics of the m-clusters of Fomin and Reading in a fashion similar to the way the cluster category of Buan, Marsh, Reineke, Reiten, and Todorov encodes the combinatorics of the clusters of(More)
The usual, or type An, Tamari lattice is a partial order on T A n , the triangulations of an (n + 3)-gon. We define a partial order on T B n , the set of centrally symmetric triangulations of a (2n + 2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the An Tamari lattice, and therefore that it deserves to be(More)