4 papers
Flag matroids: algebra and geometry
Amanda Cameron, Rodica Dinu, Mateusz Michałek +1
Matroids are ubiquitous in modern combinatorics. As discovered by Gelfand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry…
The Tutte polynomial via lattice point counting
Amanda Cameron, Alex Fink
We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and sc…
A splitter theorem for connected clutters
Amanda Cameron, Dillon Mayhew
A clutter consists of a finite set and a collection of pairwise incomparable subsets. Clutters are natural generalisations of matroids, and they have similar operations of deletion…
A lattice point counting generalisation of the Tutte polynomial
Amanda Cameron, Alex Fink
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids…