Möbius coinvariants and bipartite edge-rooted forests

Based on these interpretations, we will give new bijective proofs of the formulas for μ⊥(Km+1) and μ⊥(Km+1,n+1) given by I. Novik, A. Postnikov, and B. Sturmfels in terms of the Hermite polynomials. In addition, we will construct a homology basis for the cycle matroid complex of Km+1,n+1 indexed by the B-edge-rooted forests. Also we will discuss the Möbius coinvariant of bi-coned graphs which generalize complete bipartite graphs.