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The absolute order is a natural partial order on a Coxeter group W. It can be viewed as an analogue of the weak order on W in which the role of the generating set of simple reflections in W is played by the set of all reflections in W. By use of a notion of constructibility for partially ordered sets, it is proved that the absolute order on the symmetric… (More)

For an arbitrary Coxeter group W , Reading and Speyer defined Cambrian semi-lattices C γ as sub-semilattices of the weak order on W induced by so-called γ-sortable elements. In this article, we define an edge-labeling of C γ , and show that this is an EL-labeling for every closed interval of C γ. In addition, we use our labeling to show that every finite… (More)

In this paper we present a bijection between two well known families of Catalan objects: the set of facets of the m-generalized cluster complex ∆ m (A n) and that of dominant regions in the m-Catalan arrangement Cat m (A n), where m ∈ N >0. In particular, the map which we define bijects facets containing the negative simple root −α to dominant regions… (More)

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