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On the graph-connectivity of skeleta of convex polytopes
Christos A. Athanasiadis
Given a -dimensional convex polytope and nonnegative integer not exceeding , let denote the simple graph on the node set of -dimensional faces of i…
The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes
Christos A. Athanasiadis, Myrto Kallipoliti
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 reflect…
A combinatorial reciprocity theorem for hyperplane arrangements
Christos A. Athanasiadis
Given a nonnegative integer and a finite collection of linear forms on , the arrangement of affine hyperplanes in defined by the e…
Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes
Christos A. Athanasiadis, Eleni Tzanaki
Let be a finite root system of rank and let be a nonnegative integer. The generalized cluster complex was introduced by S. Fomin and N. Reading. It was conjec…
On the enumeration of positive cells in generalized cluster complexes and Catalan hyperplane arrangements
C. A. Athanasiadis, E. Tzanaki
Let be an irreducible crystallographic root system with Weyl group and coroot lattice , spanning a Euclidean space . Let be a positive integer and $\aA^m_…
h-vectors of generalized associahedra and non-crossing partitions
Christos A. Athanasiadis, Thomas Brady, Jon McCammond +1
A case-free proof is given that the entries of the -vector of the cluster complex , associated by S. Fomin and A. Zelevinsky to a finite root system , count elements of…