Richard P. Stanley Seminar in Combinatorics: Line shellings of geometric lattices

Inspired by Bruggesser and Mani’s line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given any nested set complex of a matroid, we show that every lexicographic ordering of the vertices of the corresponding normal complex induces a shelling order. This gives a new proof of Björner’s classical result that the order complex of the lattice of flats of a matroid is shellable, and demonstrates shellability for all nested set complexes of matroids. This talk is based on joint work with Spencer Backman, Galen Dorpalen-Barry, Anastasia Nathanson and Noah Prime.

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