Blar i forfatter "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 ...

    • Some combinatorial invariants determined by Betti numbers of Stanley-Reisner ideals 

      Roksvold, Jan Nyquist (Doctoral thesis; Doktorgradsavhandling, 2015-09-08)
      The 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 ...

    • Using pathologies as starting points for inquiry-based mathematics education: The case of the palindrome 

      Roksvold, Jan Nyquist; Haavold, Per Øystein (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-01)
      Inquiry-based mathematics education (IBME) is an increasingly important ingredient of the mathematics education in the Nordic countries. The central principle of IBME is that the students are to work in ways similar to how professional mathematicians work. In this qualitative case study, we investigate whether mathematical pathologies induce students to work like mathematicians, and thus if ...