Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions

Martin Kochol ()
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Martin Kochol: MU SAV, 814 73 Bratislava, Slovakia

Mathematics, 2023, vol. 11, issue 11, 1-10

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.

Keywords: matroid; graph; nowhere-zero flow; tension; orientation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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