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math.CO2024
The -fold circuit property for matroids
Bill Jackson, Anthony Nixon, Ben Smith
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 w…
math.CO2024
Matroids over tropical extensions of tracts
Ben Smith
A tract is an algebraic structure where multiplication is defined but addition is only partially defined. They were introduced by Baker and Bowler as a unified framework to stu…
math.CO2024
Quotients of M-convex sets and M-convex functions
Marie-Charlotte Brandenburg, Georg Loho, Ben Smith
We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a mai…