A multicomplex of partially edge-rooted forests

A coned graph Gˆ is the union of a finite graph GG and a star on its vertices. In this paper, we show that the hh-vector of the cycle matroid of Gˆ is the ff-vector of a pure multicomplex constructed from the partially edge-rooted forests in GG. This result proves a conjecture by Stanley (1996) [6] in the case of the cycle matroid of coned graphs.