|Location:||MSRI: Simons Auditorium|
We show that if a matroid is the truncation (=skeleton) of another matroid, then the generic initial ideal of its Stanley-Reisner ideal is level. In characteristic zero, the generic initial ideal is strongly stable and therefore admits an Artinian reduction by variables.
Consequently the h-vectors of truncations of matroids satisfy Stanley's
conjecture: They are Hilbert functions of Artinian monomial level algebras.
This is joint work with Alexandru Constantinescu and Matteo Varbaro.