Simplicial and cubical spanning trees

Extending an idea of Kalai, we define a spanning tree of a cell complex X as a Q-acyclic subcomplex that contains all cells of X of positive codimension. The classical matrix-tree theorem and its weighted analogues generalize to this setting, enabling us to enumerate spanning trees using Laplacians. Some applications include formulas for weighted spanning tree enumerators of skeletons of simplices and cubes, and shifted simplicial complexes. This is joint work with Art Duval and Carly Klivans.