Online Talk: Kevin Grace

YouTube recording:

Time: Thursday, July 20, 3pm ET

Speaker: Kevin Grace, Vanderbilt University
Title: Some generalizations of the class of spikes

Abstract: Spikes (also called tipless spikes in the matroid theory literature) form a well-known class of matroids that are important in the study of matroid connectivity. These matroids have the property that every pair of elements is contained in both a 4-element circuit and a 4-element cocircuit. We will present a family of generalizations of spikes, which we call (s, t)-spikes, with the property that every s-element subset of the ground set is contained in a 2s-element circuit and every t-element subset of the ground set is contained in a 2t-element cocircuit. We call this property the (s, 2s, t, 2t)-property. Our main result is that all sufficiently large matroids with the (s,2s, t, 2t)-property are (s, t)-spikes. This is joint work with Nick Brettell.

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