Blar i forfatter Artikler, rapporter og annet (matematikk og statistikk) "Roksvold, Jan Nyquist"

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    • Betti numbers associated to the facet ideal of a matroid 

      Johnsen, Trygve; Roksvold, Jan Nyquist; Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2015-01-06)
      To a matroid M with n edges, we associate the so-called facet ideal F(M)⊂k[x1,…,xn] , generated by monomials corresponding to bases of M. We show that when M is a graph, the Betti numbers related to an ℕ0-graded minimal free resolution of F(M) are determined by the Betti numbers related to the blocks of M. Similarly, we show that the higher weight hierarchy of M is determined by the weight hierarchies ...

    • A generalization of weight polynomials to matroids 

      Johnsen, Trygve; Roksvold, Jan Nyquist; Verdure, Hugues (Tidsskriftartikkel; Journal article; Peer reviewed, 2015-11-11)
      Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid M. Our main result is that these polynomials are determined by Betti numbers associated with N0-graded minimal free resolutions of the Stanley-Reisner ideals of M and so-called elongations of M. Generalizing Greene’s the- orem from coding theory, we show that ...