h-vector Inequalities Under Weak Maps

Abstract:

We study the behavior of \$h\$-vectors associated to matroid complexes under weak maps, or inclusions of matroid polytopes. Specifically, we show that the \$h\$-vector of the order complex of the lattice of flats of a matroid is component-wise non-increasing under a weak map. This result extends to the flag \$h\$-vector. We note that the analogous result also holds for independence complexes and rank-preserving weak maps.

Note:  The main talk starts at 4:10. There will be no pre-seminar.

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Meeting ID: 915 4733 5974