Mario Marietti

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In this paper we introduce and study a new class of posets, that we call zircons, which includes all Coxeter groups partially ordered by Bruhat order. We prove that many of the properties of Coxeter groups extend to zircons often with simpler proofs: in particular, zircons are Eulerian posets and the Kazhdan-Lusztig construction of the Kazhdan-Lusztig(More)
In this paper we give a purely combinatorial characterization of Coxeter groups in terms of their partial order structure under Bruhat order. The result is based on the recently introduced concept of special matching and is achieved by proving an analogue of Tits’ word theorem. As a consequence of the proof of our main result, we obtain a result about(More)
We introduce and study the notions of conical and spherical graphs. We show that these mutually exclusive properties, which have a geometric interpretation, provide links between apparently unrelated classical concepts such as dominating sets, independent dominating sets, edge covers, and the homotopy type of an associated simplicial complex. In particular,(More)