The papers in this thesis are not available in Munin:
Paper 1: Trygve Johnsen, Jan Roksvold, Hugues Verdure (2014): 'Betti numbers associated to
the facet ideal of a matroid', available in Bulletin of the Brazilian Mathematical Society 45 no. 4, 727-744
Paper 2: Trygve Johnsen, Jan Roksvold, Hugues Verdure (2014): 'A generalization of weight
polynomials to matroids', manuscript
Paper 3: Jan Roksvold, Hugues Verdure (2015): 'Betti numbers of skeletons', manuscriptThe thesis contains new results on the connection between the algebraic properties of certain ideals of a polynomial ring and properties of error-correcting linear codes, matroids and simplicial complexes. We demonstrate that the graded Betti numbers of the facet ideal of a matroid are determined by the Betti numbers of the blocks of the matroid. The extended weight enumerator of coding theory is generalized to matroids. We show that this generalization is equivalent to the Tutte-polynomial, and that the coefficients of this polynomial is determined by Betti numbers of the Stanley-Reisner ideal of the matroid and its elongations. The Betti numbers of the Stanley-Reisner ring of a skeleton of a simplicial complex is demonstrated to be an integral linear combination of the Betti numbers associated to the original complex
