Articles producció científicaEnginyeria Informàtica i Matemàtiques

A note on extension properties and representations of matroids

  • Identification data

    Identifier:  imarina:9462591
    Authors:  Bamiloshin, Michael; Farras, Oriol; Padro, Carles
    Abstract:
    We discuss several extension properties of matroids and polymatroids and their application as necessary conditions for the existence of different matroid representations, namely linear, folded linear, algebraic, and entropic representations. Iterations of those extension properties are checked for matroids on eight and nine elements by means of computer-aided explorations, finding in that way several new examples of non-linearly representable matroids. A special emphasis is made on sparse paving matroids on nine points containing the tic-tac-toe configuration. We present a new, more clear description of that family and we analyze extension properties on those matroids and their duals. (c) 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
  • Others:

    Link to the original source: https://www.sciencedirect.com/science/article/pii/S0166218X2500349X?via%3Dihub
    APA: Bamiloshin, Michael; Farras, Oriol; Padro, Carles (2025). A note on extension properties and representations of matroids. Discrete Applied Mathematics, 376(), 270-280. DOI: 10.1016/j.dam.2025.06.028
    Paper original source: Discrete Applied Mathematics. 376 270-280
    Article's DOI: 10.1016/j.dam.2025.06.028
    Journal publication year: 2025
    Entity: Universitat Rovira i Virgili
    Paper version: info:eu-repo/semantics/publishedVersion
    Record's date: 2025-08-02
    URV's Author/s: Farràs Ventura, Oriol
    Department: Enginyeria Informàtica i Matemàtiques
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Publication Type: Journal Publications
    Author, as appears in the article.: Bamiloshin, Michael; Farras, Oriol; Padro, Carles
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Thematic Areas: Applied mathematics, Ciência da computação, Ciências biológicas i, Discrete mathematics and combinatorics, Engenharias i, Engenharias iii, Engenharias iv, Ensino, Interdisciplinar, Linguística e literatura, Matemática / probabilidade e estatística, Mathematics, applied
    Author's mail: oriol.farras@urv.cat
  • Keywords:

    Bound
    Common information
    Entropy
    Generalized euclidean property
    Inequalities
    Information
    Matroid representation
    Networks
    Secret sharing scheme
    Secret sharing schemes
    Applied Mathematics
    Discrete Mathematics and Combinatorics
    Mathematics
    Applied
    Ciência da computação
    Ciências biológicas i
    Engenharias i
    Engenharias iii
    Engenharias iv
    Ensino
    Interdisciplinar
    Linguística e literatura
    Matemática / probabilidade e estatística
  • Documents:

  • Cerca a google

    Search to google scholar