The Veronese Construction for Formal Power Series and Graded Algebras (2007)
Brenti, Francesco, Welker, Volkmar
Let $(a_n)_{n \geq 0}$ be a sequence of complex numbers such that its generating series satisfies $\sum_{n \geq 0} a_nt^n = \frac{h(t)}{(1-t)^d}$ for some polynomial $h(t)$. For any $r \geq 1$ we...
Complexes of Injective Words and Their Commutation Classes (2007)
Jonsson, Jakob, Welker, Volkmar
Let $S$ be a finite alphabet. An injective word over $S$ is a word over $S$ such that each letter in $S$ appears at most once in the word. We study Boolean cell complexes of injective words over $S$...
On Sequentially Cohen-Macaulay Complexes and Posets (2007)
Björner, Anders, Wachs, Michelle, Welker, Volkmar
The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy...
Type-B generalized triangulations and determinantal ideals (2006)
For $n\geq 3$, let $\Omega_n$ be the set of line segments between the vertices of a convex $n$-gon. For $j\geq 2$, a $j$-crossing is a set of $j$ line segments pairwise intersecting in the relative...
$f$-Vectors of Barycentric Subdivisions (2006)
Brenti, Francesco, Welker, Volkmar
For a simplicial complex or more generally Boolean cell complex $\Delta$ we study the behavior of the $f$- and $h$-vector under barycentric subdivision. We show that if $\Delta$ has a non-negative...
The Multiplicity Conjecture for Barycentric Subdivisions (2006)
Kubitzke, Martina, Welker, Volkmar
For a simplicial complex $\Delta$ we study the effect of barycentric subdivision on ring theoretic invariants of its Stanley-Reisner ring. In particular, for Stanley-Reisner rings of barycentric...
Resolution of the residue class field via algebraic discrete Morse theory (2005)
Joellenbeck, Michael, Welker, Volkmar
Forman's Discrete Morse theory is studied from an algebraic viewpoint. Analogous to independent work of Emil Skoeldberg we show that this theory can be extended to chain complexes of free modules...
Complexes of graphs with bounded matching size (2004)
Linusson, Svante, Shareshian, John, Welker, Volkmar
For positive integers k,n, we investigate the simplicial complex NM_k(n) of all graphs G on vertex set [n] such that every matching in G has size less than k. This complex (along with other...
Segre and Rees products of posets, with ring-theoretic applications (2003)
Björner, Anders, Welker, Volkmar
We introduce (weighted) Segre and Rees products for posets and show that these constructions preserve the Cohen-Macaulay property over a field $k$ and homotopically. As an application we show that...
Hersh, Patricia, Welker, Volkmar
The purpose of this paper is twofold. 1. We give combinatorial bounds on the ranks of the groups $\Tor^{R}_\bullet(k,k)_\bullet$ in the case where $R = k[\Lambda]$ is an affine semi-group ring, and...
Computing Simplicial Homology Based on (2002)
Ecient Smith, Normal Form Algorithms, Frank Heckenbach, David Saunders, Volkmar Welker
We recall that the calculation of homology with integer coecients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We...
Local Cohomology Of Stanley-Reisner Rings With Supports In General Monomial Ideals (2000)
this paper, we construct an analogous theory for a Stanley-Reisner ring k[] using combinatorial topology. Let S = k[x 1 ; : : : ; x n ] be a polynomial ring over a eld k. Let 2
Simplicial Homology - A proposed share package for GAP (2000)
Simplicial Homology, Jean-guillaume Dumas, Frank Heckenbach, David Saunders, Volkmar Welker
eorems. It is our expectation that working with the package will allow many application of that kind. The functionality of GAP 4 fits perfectly in this picture. The algebraic and combinatorial...
Joachim Hornegger, Volkmar Welker, Heinrich Niemann
In general, projections as input data for 3--D object recognition algorithms do not simplify the problem due to the loss of range information. However, in this work we demonstrate that this...
The LCM-Lattice in Monomial Resolutions (1999)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
this paper we obtain results on the minimal free resolution of an arbitrary monomial ideal. We introduce a new approach inspired by the topological theory of subspace arrangements. Some of the best...
THE LCM-LATTICE in MONOMIAL RESOLUTIONS (1999)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
Introduction Describing the properties of the minimal free resolution of a monomial ideal I is a difficult problem posed in the early 1960's. The main directions of progress on this problem were: ffl...
Localization and Classification Based on Projections (1999)
Joachim Hornegger, Volkmar Welker, Heinrich Niemann
In general, projections as input data for 3--D object recognition algorithms do not simplify the problem due to the loss of range information. However, in this work we demonstrate that this...
Rationality For Generic Toric Rings (1998)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
: We study generic toric rings. We prove that they are Golod rings, so the Poincar'e series of the residue field is rational. We classify when such a ring is Koszul, and compute its rate. Also...
Coordinate Subspace Arrangements and Monomial Ideals (1998)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
: We relate the (co)homological properties of real coordinate subspace arrangements and of monomial ideals. 1. Introduction In [PRW] we describe the cohomological properties of a real diagonal...
RATIONALITY FOR GENERIC TORIC RINGS Vesselin Gasharov Irena Peeva Volkmar Welker (1998)
Vesselin Gasharov, Irena Peeva, Volkmar Welker
: We study generic toric rings. We prove that they are Golod rings, so the Poincar'e series of the residue field is rational. We classify when such a ring is Koszul, and compute its rate. Also...
A Homological Lower Bound For Order Dimension Of Lattices (1998)
We prove that if a finite lattice L has order dimension at most d, then the homology of the order complex of its proper part L ffi vanishes in dimensions d - 1 and higher. In case L can be embedded...
Cohomology Of Real Diagonal Subspace Arrangements Via Resolutions (1998)
Irena Peeva, Vic Reiner, Volkmar Welker
: We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Homotopy Colimits - Comparison Lemmas for Combinatorial Applications (1997)
Volkmar Welker, Gunter M. Ziegler, Rade T
We provide a "toolkit" of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used on quite different...
Cohomology Of Real Diagonal Subspace Arrangements Via Resolutions (1997)
Irena Peeva, Vic Reiner, Volkmar Welker
We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the...
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...
Group Actions on Arrangements of Linear Subspaces and Applications to Configuration Spaces (1997)
Sheila Sundaram, Volkmar Welker
this paper we develop combinatorial and representation-theoretic methods in the theory of arrangements of linear subspaces in R , which can be applied to the study of the cohomology of spaces of...
The Homology of "k-equal" Manifolds and Related Partition Lattices (1997)
Anders Bj Orner, Volkmar Welker
this paper is to obtain topological and combinatorial information about these subspace arrangements and the manifolds M n;k = R n;k = C n;k
The Koszul Property In Affine Semigroup Rings (1997)
J Herzog, Vic Reiner, Volkmar Welker
We investigate the Koszul property for quotients of affine semigroup rings by semigroup ideals. Using a combinatorial and topological interpretation for the Koszul property in this context, we...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Colored Partitions and a Generalization of the Braid Arrangement (1997)
We study the topology and combinatorics of an arrangement of hyperplanes in C n that generalizes the classical braid arrangement. The arrangement plays in important role in the work of Schechtman &...
Welker, Volkmar, Shapiro, Boris
We study the stratification of the space of monic polynomials with real coefficients according to the number and multiplicities of real zeros. In the first part, for each of these strata we provide a...
Comparison Lemmas and Applications for Diagrams of Spaces (1970)
Volkmar Welker, Gunter M. Ziegler, Rade T
We provide a "toolkit" of basic lemmas for the comparison of homotopy types of (homotopy) limits of diagrams of spaces over finite partially ordered sets, among them several new ones. In the setting...