The Hepp bound, a rational matroid invariant from tropicalizing the Feynman period integral, provably respects all known graph period symmetries and correlates strongly with actual periods.
The Lattice of Cyclic Flats of a Matroid
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A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the perspective of cyclic flats. In particular, we show that every lattice is isomorphic to the lattice of cyclic flats of a matroid. We give a necessary and sufficient condition for a lattice Z of sets and a function r on Z to be the lattice of cyclic flats of a matroid and the restriction of the corresponding rank function to Z. We define cyclic width and show that this concept gives rise to minor-closed, dual-closed classes of matroids, two of which contain only transversal matroids.
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Hepp's bound for Feynman graphs and matroids
The Hepp bound, a rational matroid invariant from tropicalizing the Feynman period integral, provably respects all known graph period symmetries and correlates strongly with actual periods.