An overview of the computational aspects of nonunique factorization invariants

Preprint English OPEN
García-Sánchez, P. A.;
(2015)
  • Subject: Mathematics - Combinatorics | Mathematics - Commutative Algebra | 20M13, 20M14
    acm: TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES | TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS
    arxiv: Mathematics::Category Theory

We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.
  • References (41)
    41 references, page 1 of 5

    [1] 4ti2 team, 4ti2-a software package for algebraic, geometric and combinatorial problems on linear spaces, available at www.4ti2.de.

    [2] M. Barakat, S. Gutsche, S. Jambor, M. Lange-Hegermann, A. Lorenz and O. Motsak, GradedModules, A homalg based package for the Abelian category of finitely presented graded modules over computable graded rings, Version 2014.09.17 (2014), ((GAP package)), http://homalg.math.rwth-aachen.de.

    [3] T. Barron, C. O'Neill, R. Pelayo, On the computation of delta sets and ω-primality in numerical monoids, preprint, 2014

    [4] V. Blanco, P. A. García-Sánchez, A. Geroldinger, Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids, Illinois J. Math. 55 (2011), 1385-1414.

    [5] W. Bruns, B. Ichim, T. Römer, and C. Söger, Normaliz, algorithms for rational cones and affine monoids, http://www.math.uos.de/normaliz, 2014.

    [6] L. Bryant, J. Hamblin, The maximal denumerant of a numerical semigroup, Semigroup Forum 86 (2013), 571-582.

    [7] M. Bullejos, P. A. García-Sánchez, Minimal presentations for monoids with the ascending chain condition on principal ideals, Semigroup Forum 85 (2012), 185-190.

    [8] S. T. Chapman, M. Corrales, A. Miller, C. Miller, and D. Phatel, The catenary and tame degrees on a numerical monoid are eventually periodic, J. Aust. Math. Soc. 97 (2014), 289-300.

    [9] S. T. Chapman, P. A. García-Sánchez, D. Llena, The catenary and tame degree of a numerical semigroup, Forum Math. 21 (2009), 117-129.

    [10] S. T. Chapman, P. A. García-Sánchez, D. Llena, V. Ponomarenko, J. C. Rosales, The catenary and tame degree in finitely generated commutative cancellative monoids, Manuscripta Math. 120 (2006), 253-264.

  • Related Research Results (3)
  • Metrics
Share - Bookmark