Lefschetz Properties and Basic Constructions on Simplicial Spheres (2008)
The well known $g$-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the...
The fundamental group of random 2-complexes (2007)
Babson, Eric, Hoffman, Christopher, Kahle, Matthew
The random 2-complex Y=Y(n,p) is the probability space of all simplicial complexes on vertex set [n] and edge set [n] \choose 2, with each 2-dimensional face included with probability p...
Reconstructing Metric Trees from Order Information on Triples is NP Complete (2006)
We show that reconstructing a tree from order information on triples is NP-hard. This is in contrast to the case for ultra-metrics and for subtree information on quadruples which are both known to...
Reverse Lexicographic and Lexicographic Shifting (2005)
Babson, Eric, Novik, Isabella, Thomas, Rekha R.
A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, $\Delta_{\lex}$ -- an operation that transforms a...
Proof of the Lovasz Conjecture (2004)
Babson, Eric, Kozlov, Dmitry N.
To any two graphs G and H one can associate a cell complex Hom(G,H) by taking all graph multihomorphisms from G to H as cells. In this paper we prove the Lovasz Conjecture which states that if...
Motivated by the Coxeter complex associated to a Coxeter system (W, S), we introduce a simplicial regular cell complex #(G,S) with a G-action associated to any pair (G, S) where G is a group and S is...
Discrete Morse functions from lexicographic orders (2003)
This paper shows how to construct a discrete Morse function with a relatively small number of critical cells for the order complex of any finite poset with $\hat{0} $ and $\hat{1}$ from any...
Group Actions on Posets (2003)
Babson, Eric, Kozlov, Dmitry N.
In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories...
Complexes of graph homomorphisms (2003)
Babson, Eric, Kozlov, Dmitry N.
$Hom(G,H)$ is a polyhedral complex defined for any two undirected graphs $G$ and $H$. This construction was introduced by Lov\'asz to give lower bounds for chromatic numbers of graphs. In this paper...
Topological obstructions to graph colorings (2003)
Babson, Eric, Kozlov, Dmitry N.
For any two graphs $G$ and $H$ Lov\'asz has defined a cell complex $Hom(G,H)$ having in mind the general program that the algebraic invariants of these complexes should provide obstructions to graph...
Geometry of the tetrahedron space (2002)
Babson, Eric, Gunnells, Paul E., Scott, Richard
Let X^{circ} be the space of all labeled tetrahedra in P^{3}. In [BGS] we constructed a smooth symmetric compactification X-tilde of X^{circ}. In this article we show that the complement X-tilde...
The Hilbert Zonotope and a Polynomial Time Algorithm for Universal Grobner Bases (2002)
Babson, Eric, Onn, Shmuel, Thomas, Rekha
We provide a polynomial time algorithm for computing the universal Gr\"obner basis of any polynomial ideal having a finite set of common zeros in fixed number of variables. One ingredient of our...
Symmetric iterated Betti numbers (2002)
Babson, Eric, Novik, Isabella, Thomas, Rekha
We define a set of invariants of a homogeneous ideal $I$ in a polynomial ring called the symmetric iterated Betti numbers of $I$. For $I_{\Gamma}$, the Stanley-Reisner ideal of a simplicial complex...
Group Actions On Posets (2002)
In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories...
Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids (2000)
Eric Babson, Lukas Finschi, Komei Fukuda
We consider the cocircuit graph GM of an oriented matroid M, which is the 1-skeleton of the cell complex formed by the span of the cocircuits of M. As a result of Cordovil, Fukuda, and Guedes de...
Generalized permutation patterns and a classification of the Mahonian statistics (2000)
We introduce generalized permutation patterns, where we allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We show that essentially all Mahonian...
Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids (2000)
Eric Babson, Lukas Finschi, Komei Fukuda
We consider the cocircuit graph GM of an oriented matroid M, which is the 1-skeleton of the cell complex formed by the span of the cocircuits of M. As a result of Cordovil, Fukuda, and Guedes de...
A smooth space of tetrahedra (1999)
Babson, Eric, Gunnells, Paul E., Scott, Richard
We construct a smooth symmetric compactification of the space of all labeled tetrahedra in P^3.
Complexes Of Not i-Connected Graphs (1998)
Eric Babson, Anders Bj Orner, Svante Linusson
. Complexes of (not) connected graphs, hypergraphs and their homology appear in the construction of knot invariants given by V. Vassiliev [V1, V2, V4]. In this paper we study the complexes of not...
Diagrams Of Classifying Spaces And k-Fold Boolean Algebras (1998)
. In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a...
Complexes of not $i$-connected graphs (1997)
Babson, Eric, Björner, Anders, Linusson, Svante, Shareshian, John, Welker, Volkmar
Complexes of (not) connected graphs, hypergraphs and their homology appear in the construction of knot invariants given by V. Vassiliev. In this paper we study the complexes of not $i$-connected...
Diagrams of classifying spaces and $k$-fold Boolean algebras (1997)
In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a...