6 papers
-fold circuits and coning in rigidity matroids
John Hewetson, Bill Jackson, Anthony Nixon +1
In 1980 Lovász introduced the concept of a double circuit in a matroid. The 2nd, 3rd and 4th authors recently generalised this notion to -fold circuits (for any natural number…
Characterisations of strong -matroids
Kieran Calvert, Aram Dermenjian, Alex Fink +1
We study characterisations of strong -matroids, compiling a list of five equivalent descriptions. We show a variant of Wenzel's exchange property and the hyperplane exchange pr…
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…
Quadratic exchange equations for Coxeter matroids
Kieran Calvert, Aram Dermenjian, Alex Fink +1
Tropicalisation (with trivial coefficients) is a process that turns a polynomial equation into a combinatorial predicate on subsets of the set of variables. We show that for each m…
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…
Allowed Coulomb branch scaling dimensions of four-dimensional SCFTs
Philip C. Argyres, Sergio Cecotti, Michele Del Zotto +3
A basic datum of a rank- superconformal field theory (SCFT) is the -tuple of its Coulomb branch scaling dimensions, i.e., the scaling dimensions of a set of…