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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: • constructing the minimal free resolutions of special monomial ideals, cf. [AHH, BPS] • constructing non-minimal free resolutions; for example, Taylor’s resolution (cf. [Ei,… (More)

- Victor Reiner, Volkmar Welker
- J. Comb. Theory, Ser. A
- 2005

For a graded naturally labelled poset P , it is shown that the P -Eulerian polynomial

Complexes of (not) connected graphs, hypergraphs and their ho-mology appear in the construction of knot invariants given by V. Vassiliev V1, V2, V4]. In this paper we study the complexes of not i-connected k-hypergraphs on n vertices. We show that the complex of not 2-connected graphs has the homotopy type of a wedge of (n ? 2)! spheres of dimension 2n ? 5.… (More)

- Volkmar Welker, Rade T. Zivaljevi
- 1997

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 diierent elds of applications. We demonstrate this with respect to 1. Bjj orner's \Generalized Homotopy Complementation Formula" 4], 2. the topology of toric varieties, 3.… (More)

- Anders Björner, Volkmar Welker
- SIAM J. Discrete Math.
- 1999

- Volkmar Welker
- Discrete Mathematics
- 1999

- Jean-Guillaume Dumas, Frank Heckenbach, B. David Saunders, Volkmar Welker
- Algebra, Geometry, and Software Systems
- 2003

We recall that the calculation of homology with integer coefficients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices and compare their running times for actual boundary… (More)

Let (an)n≥0 be a sequence of complex numbers such that its generating series satisfies ∑ n≥0 ant n = h(t) (1−t)d for some polynomial h(t). For any r ≥ 1 we study the transformation of the coefficient series of h(t) to that of h〈r〉(t) where ∑ n≥0 anrt n = h 〈r〉(t) (1−t)d . We give a precise description of this transformation and show that under some natural… (More)

- Paul H. Edelman, Victor Reiner, Volkmar Welker
- Discrete & Computational Geometry
- 2002

- Vic Reiner, Volkmar Welker
- 1997

We investigate the Koszul property for quotients of aane semigroup rings by semigroup ideals. Using a combinatorial and topological interpretation for the Koszul property in this context, we recover known results asserting that certain of these rings are Koszul. In the process, we prove a stronger fact, suggesting a more general deenition of Koszul rings.… (More)