Myrto Kallipoliti

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The absolute order on the hyperoctahedral group Bn is investigated. Using a poset fiber theorem, it is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen–Macaulay. This method results in a new proof of Cohen–Macaulayness of the absolute order on the symmetric group. Moreover, it is shown that every closed interval(More)
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 semilattices Cγ as sub-semilattices of the weak order onW induced by so-called γ-sortable elements. In this article, we define an edge-labeling of Cγ , and show that this is an EL-labeling for every closed interval of Cγ . In addition, we use our labeling to show that every finite open(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 ∆(An) and that of dominant regions in the m-Catalan arrangement Cat(An), where m ∈ N>0. In particular, the map which we define bijects facets containing the negative simple root −α to dominant regions having the(More)
For an arbitrary Coxeter group W , David Speyer and Nathan Reading defined Cambrian semilattices Cγ as certain sub-semilattices of the weak order on W . In this article, we define an edge-labeling using the realization of Cambrian semilattices in terms of γ-sortable elements, and show that this is an EL-labeling for every closed interval of Cγ . In(More)
In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extends the well-known result that those posets are shellable. Both results rely on a(More)
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