We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the higher dimensional spanning trees in a class of cell complexes. This gives a new proof of Tutte’s theorem that the number of spanning trees of a central reflex is a perfect square and solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted… CONTINUE READING