Athanasiadis, Christos A., Welker, Volkmar
A class of simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay...
Some combinatorial properties of flag simplicial pseudomanifolds and spheres (2008)
A simplicial complex $\Delta$ is called flag if all minimal nonfaces of $\Delta$ have at most two elements. The following are proved: (i) if $\Delta$ is a flag simplicial pseudomanifold of dimension...
Shellability of noncrossing partition lattices (2008)
Christos A. Athanasiadis, Thomas Brady, Colum Watt
Abstract. We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups...
h ∗ -vectors, Eulerian polynomials and stable polytopes of graphs, Electron (2008)
Conditions are given on a lattice polytope P of dimension m or its associated affine semigroup ring which imply inequalities for the h∗-vector (h ∗ 0,h∗1,...,h∗m)of P of the form h ∗ i ≥...
Projections of polytopes on the plane and the generalized Baues problem (2008)
Abstract. Given an affine projection π: P → Q of a d-polytope P onto a polygon Q, it is proved that the poset of proper polytopal subdivisions of Q which are induced by π has the homotopy type of...
On some enumerative aspects of generalized associahedra (2008)
Abstract. We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice...
THE GENERALIZED BAUES PROBLEM FOR CYCLIC POLYTOPES II (2008)
Cyclic Polytopes Ii, Christos A. Athanasiadis, Francisco Santos, The Generalized
WHICH ARE INDUCED BY THE MAP has the homotopON tS Ope of A SPHERE. WE EXTEND earlier work of the last two authors on subdivisio of cyclic polBEtopes to YCive an affirmative answer to the problem for...
Noncrossing partitions for the group Dn (2008)
Christos A. Athanasiadis, Victor Reiner
Dedicated to the memory of Rodica Simion Abstract. The poset of noncrossing partitions can be naturally defined for any finite Coxeter group W. It is a self-dual, graded lattice which reduces to the...
Noncrossing partitions for the group Dn (2008)
Christos A. Athanasiadis, Victor Reiner
Dedicated to the memory of Rodica Simion Abstract. The poset of noncrossing partitions can be naturally defined for any finite Coxeter group W. It is a self-dual, graded lattice which reduces to the...
On the graph-connectivity of skeleta of convex polytopes (2008)
Given a $d$-dimensional convex polytope $P$ and nonnegative integer $k$ not exceeding $d-1$, let $G_k (P)$ denote the simple graph on the node set of $k$-dimensional faces of $P$ in which two such...
On The Topology Of The Baues Poset Of Polyhedral Subdivisions (2007)
Christos Athanasiadis And, Christos A. Athanasiadis, Francisco Santos
. Given an affine projection : P ! Q of convex polytopes, let !(P; ) be the refinement poset of proper polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let !...
Piles Of Cubes, Monotone Path Polytopes And Hyperplane Arrangements (2007)
. Monotone path polytopes arise as a special case of the construction of fiber polytopes, introduced by Billera and Sturmfels. A simple example is provided by the permutahedron, which is a monotone...
Monotone Paths On Zonotopes And Oriented Matroids (2007)
Christos A. Athanasiadis, FRANCISCO SANTOS
. Monotone paths on zonotopes and the natural generalization to maximal chains in the poset of topes of an oriented matroid or arrangement of pseudo-hyperplanes are studied with respect to a kind of...
Athanasiadis, Christos A., Kallipoliti, Myrto
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...
A combinatorial reciprocity theorem for hyperplane arrangements (2006)
Given a nonnegative integer $m$ and a finite collection ${\mathcal A}$ of linear forms on ${\mathbb Q}^d$, the arrangement of affine hyperplanes in ${\mathbb Q}^d$ defined by the equations $\alpha(x)...
Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes (2006)
Athanasiadis, Christos A., Tzanaki, Eleni
Let $\Phi$ be a finite root system of rank $n$ and let $m$ be a nonnegative integer. The generalized cluster complex $\Delta^m (\Phi)$ was introduced by S. Fomin and N. Reading. It was conjectured by...
h-vectors of generalized associahedra and non-crossing partitions (2006)
Athanasiadis, Christos A., Brady, Thomas, McCammond, Jon, Watt, Colum
A case-free proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the...
h-vectors of generalized associahedra and noncrossing partitions (2006)
Athanasiadis, Christos A., Brady, Thomas, McCammond, Jon, Watt, Colum
A uniform proof is given that the entries of the h-vector of the cluster complex Δ(Φ), associated by S. Fomin and A. Zelevinsky to a finite root system Φ, count elements of the lattice L of...
On some enumerative aspects of generalized associahedra (2005)
We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice of...
Shellability of noncrossing partition lattices (2005)
Athanasiadis, Christos A., Brady, Thomas, Watt, Colum
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type...
Shellability of noncrossing partition lattices (2005)
Athanasiadis, Christos A., Brady, Thomas, Watt, Colum
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type Dn...
Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley (2003)
It is proved that a certain symmetric sequence of nonnegative integers arising in the enumeration of magic squares of given size n by row sums or, equivalently, in the generating function of the...
Zonotopal Subdivisions of Cyclic Zonotopes (2000)
. The cyclic zonotope Z(n; d) is the zonotope in R d generated by any n distinct vectors of the form (1; t; t 2 ; : : : ; t d\Gamma1 ). It is proved that the refinement poset of all proper zonotopal...
On The Topology Of The Baues Poset Of Polyhedral Subdivisions (2000)
Christos A. Athanasiadis, Francisco Santos
. Given an affine projection : P ! Q of convex polytopes, let !(P; ) be the refinement poset of proper polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let !...
Zonotopal Subdivisions of Cyclic Zonotopes (2000)
The cyclic zonotope Z(n, d) is the zonotope in R^d generated by any n distinct vectors of the form (1, t, t², ..., t^d-1). It is proved that the refinement poset of all proper zonotopal...
The generalized Baues problem for cyclic polytopes II (1999)
Christos A. Athanasiadis, Jörg Rambau, Francisco Santos
Given an affine surjection of polytopes : P! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map has the homotopy type of a...
Projections Of Polytopes On The Plane And The Generalized Baues Problem (1999)
. Given an affine projection : P ! Q of a d-polytope P onto a polygon Q, it is proved that the poset of proper polytopal subdivisions of Q which are induced by has the homotopy type of a sphere of...
The Generalized Baues Problem for Cyclic Polytopes II (1999)
Preprint Sc Januar, Christos A. Athanasiadis, Christos A. Athanasiadis, J Org Rambau, J Org Rambau, Francisco Santos, ...
. Given an affine surjection of polytopes ß : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map ß has the homotopy...
On free deformations of the braid arrangement (1998)
We classify the hyperplane arrangements between the cones of the braid arrangement and the Shi arrangement of type An−1 which are free, in the sense of Terao. We also prove that the cones of the...
Deformations of Coxeter hyperplane arrangements and their characteristic polynomials (1998)
. Let A be a Coxeter hyperplane arrangement, that is the arrangement of reflecting hyperplanes of an irreducible finite Coxeter group. A deformation of A is an a#ne arrangement each of whose...
On Noncrossing and Nonnesting Partitions for Classical Reflection Groups (1998)
. The number of noncrossing partitions of {1, 2,... ,n}with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonnesting partitions. We...
The Generalized Baues Problem For Cyclic Polytopes II (1998)
Christos A. Athanasiadis, Jörg Rambau, J Org Rambau, Francisco Santos
. Given an affine surjection of polytopes ß : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map ß has the homotopy...
On Noncrossing and Nonnesting Partitions for Classical Reflection Groups (1998)
. The number of noncrossing partitions of f1; 2; : : : ; ng with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonnesting partitions....
Deformations of Coxeter hyperplane arrangements and their characteristic polynomials (1998)
Let A be a Coxeter hyperplane arrangement, that is the arrangement of reflecting hyperplanes of an irreducible finite Coxeter group. A deformation of A is an affine arrangement each of whose...
A hyperplane arrangement is said to satisfy the ``Riemann hypothesis'' if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley...
A Simple Bijection for the Regions of the Shi Arrangement of Hyperplanes (1997)
Athanasiadis, Christos A., Linusson, Svante
The Shi arrangement ${\mathcal S}_n$ is the arrangement of affine hyperplanes in ${\mathbb R}^n$ of the form $x_i - x_j = 0$ or $1$, for $1 \leq i < j \leq n$. It dissects ${\mathbb R}^n$ into...
Piles of Cubes, Monotone Path Polytopes and Hyperplane Arrangements (1997)
Monotone path polytopes arise as a special case of the construction of fiber polytopes, introduced by Billera and Sturmfels. A simple example is provided by the permutahedron, which is a monotone...
Christos A. Athanasiadis, Mb Ma Mc
We consider the class Pn of labeled posets on n elements which avoid certain three-element induced subposets. We show that the number of posets in Pn is (n+1) n&1 by exploiting a bijection...
Fiber Polytopes For The Projections Between Cyclic Polytopes (1997)
Christos Athanasiadis Jes, Christos A. Athanasiadis, Victor Reiner, Francisco Santos
. The cyclic polytope C(n; d) is the convex hull of any n points on the moment curve f(t; t 2 ; : : : ; t d ) : t 2 Rg in R d . For d 0 ? d, we consider the fiber polytope (in the sense of Billera...
On Free Deformations of the Braid Arrangement (1997)
We classify the hyperplane arrangements between the cones of the braid arrangement and the Shi arrangement of type A n\Gamma1 which are free, in the sense of Terao. We also prove that the cones of...
A Simple Bijection For The Regions Of The Shi Arrangement Of Hyperplanes (1997)
Christos A. Athanasiadis, Svante Linusson
. The Shi arrangement Sn is the arrangement of affine hyperplanes in R n of the form x i \Gamma x j = 0 or 1, for 1 i ! j n. It dissects R n into (n+1) n\Gamma1 regions, as was first proved by Shi....
Piles Of Cubes, Monotone Path Polytopes And Hyperplane Arrangements (1997)
. Monotone path polytopes arise as a special case of the construction of fiber polytopes, introduced by Billera and Sturmfels. A simple example is provided by the permutahedron, which is a monotone...
Fiber Polytopes For The Projections Between Cyclic Polytopes (1997)
Christos A. Athanasiadis, Victor Reiner, Francisco Santos
. The cyclic polytope C(n; d) is the convex hull of any n points on the moment curve f(t; t 2 ; : : : ; t d ) : t 2 Rg in R d . For d 0 ? d, we consider the fiber polytope (in the sense of Billera...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
Algebraic combinatorics of graph spectra, subspace arrangements and Tutte polynomials (1996)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
Algebraic combinatorics of graph spectra, subspace arrangements and Tutte polynomials (1996)
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
Christos A. Athanasiadis, Paul H. Edelman, Victor Reiner
. We investigate the vertex-connectivity of the graph of f-monotone paths on a d-polytope P with respect to a generic functional f . The third author has conjectured that this graph is always (d...
A Simple Bijection For The Regions Of The Shi Arrangement Of Hyperplanes
Christos A. Athanasiadis, Svante Linusson
. The Shi arrangement Sn is the arrangement of affine hyperplanes in R n of the form x i \Gamma x j = 0 or 1, for 1 i ! j n. It dissects R n into (n+1) n\Gamma1 regions, as was first proved by Shi....
Christos A. Athanasiadis, Paul H. Edelman, Victor Reiner
. We investigate the vertex-connectivity of the graph of f-monotone paths on a d-polytope P with respect to a generic functional f . The third author has conjectured that this graph is always (d...