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Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions

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  • Martin Kochol

    (MU SAV, 814 73 Bratislava, Slovakia)

Abstract

We introduce a unifying approach for invariants of finite matroids that count mappings to a finite set. The aim of this paper is to show that if the cardinalities of mappings with fixed values on a restricted set satisfy contraction–deletion rules, then there is a relation among them that can be expressed in terms of linear algebra. In this way, we study regular chain groups, nowhere-zero flows and tensions on graphs, and acyclic and totally cyclic orientations of oriented matroids and graphs.

Suggested Citation

  • Martin Kochol, 2023. "Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions," Mathematics, MDPI, vol. 11(11), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2570-:d:1163372
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    References listed on IDEAS

    as
    1. BLAND, Robert G. & LAS VERGNAS, Michel, 1978. "Orientability of matroids," LIDAM Reprints CORE 326, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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