2008/03/04 by Eduardo Sáenz‐de‐Cabezón, Eduardo Saenz-de-Cabezon, Saenz-de-Cabezon, Eduardo
Computer Science · Mathematics · #13D02 #13P10 #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.AC #msc:13D02 #msc:13P10
paper · pdf · doi:10.48550/arxiv.0803.0421
PhD Thesis
arxiv created 2008/03/04 · openalex publication_date 2008/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals of this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the structure of monomial ideals. Describe algorithms to perform efficient computations of the homological invariants of monomial ideals. Apply the theory and computations on monomial ideals to problems inside and outside mathematics The thesis introduces as a main tool Mayer-Vietoris trees of monomial ideals.