In Stanley’s seminal work “Cohen-Macaulay Complexes”, Stanley conjectured that all h vectors of matroid complexes are pure O-sequences. We constructed coparking functions on matroids with extra restrictions and showed that the degree sequences of coparking functions are the same as h vectors of matroid complexes. By this construction, we proved that Stanley’s conjecture is true for matroids which admit “circuits system”. Our construction of coparking functions is the dual version of Postnikov and Shapiro’s construction of G-parking functions on graphs. In this talk, we will explain the connection with Postnikov and Shapiro’s construction and explain the main idea for the proof which utilizes the deletion/contraction relation of Tutte polynomials. This is a joint work with Anton Dochtermann.

Speaker’s webpage: https://sites.duke.edu/ypli/