2024/12/19 by Bill Jackson, Anthony Nixon, Jackson, Bill +3 · 1 citation
Computer Science · #05B35 #06C10 #90C27 #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Machine Learning and Algorithms #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2412.14782
openalex publication_date 2024/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Double circuits were introduced by Lovász in 1980 as a fundamental tool in his derivation of a min-max formula for the size of a maximum matching in linear matroids. This formula was extended to all matroids satisfying the so-called `double circuit property' by Dress and Lovász in 1987. We extend these notions to k-fold circuits for all natural numbers k and show, in particular that several families of matroids which are known to satisfy the double circuit property, satisfy the k-fold circuit property for all natural numbers k. These families include all pseudomodular matroids (such as full linear, algebraic and transversal matroids) and certain families of count matroids. These results suggest that the k-fold circuit property can be used as a measure of how close the lattice of flats of a matroid is to being a modular lattice.