Sökning: "Volkmar Welker"
Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Volkmar Welker.
1. On properties of monomial ideals and algebras
Sammanfattning : Monomial ideals form an important link between commutative algebra and combinatorics. Our aim is to study various operations on monomial ideals and algebras, as well as their properties. This thesis consists of an introduction and four research articles. The introduction covers the necessary background and the existing results. LÄS MER
2. On Face Vectors and Resolutions
Sammanfattning : This thesis consist of the following three papers.Convex hull of face vectors of colored complexes. In this paper we verify a conjecture by Kozlov (Discrete ComputGeom18(1997) 421–431), which describes the convex hull of theset of face vectors ofr-colorable complexes onnvertices. LÄS MER
3. Topological and Shifting Theoretic Methods in Combinatorics and Algebra
Sammanfattning : This thesis consists of six papers related to combinatorics and commutative algebra.In Paper A, we use tools from topological combinatorics to describe the minimal free resolution of ideals with a so called regular linear quotient. Our result generalises the pervious results by Mermin and by Novik, Postnikov & Sturmfels. LÄS MER
4. Ekedahl Invariants, Veronese Modules and Linear Recurrence Varieties
Sammanfattning : The title of this thesis refers to the three parts of which it is composed.The first part concerns the Ekedahl Invariants, new geometric invariants for finite groups introduced in 2009 by Torsten Ekedahl. LÄS MER
5. Around power ideals : From Fröberg's conjecture to zonotopal algebra
Sammanfattning : In this thesis we study power algebras, which are quotient of polynomial rings by power ideals. We will study Hilbert series of such ideals and their other properties. We consider two important special cases, namely, zonotopal ideals and generic ideals. Such ideals have a lot combinatorial properties. LÄS MER