Georgia Institute of Technology College of Sciences

Let G be a graph. Backman, Baker, and Yuen have constructed a family of bijections between spanning trees of G and the equivalence classes of orientations up to cycle-cocycle reversal, called the geometric bijections. Their proof makes use of zonotopal subdivisions. Recently we have extended the geometric bijections to subgraph-orientation correspondences. Moreover, we have also constructed a larger family of bijections, which contains the geometric bijections and the Bernardi bijections. Most of our work is inspired by geometry but proved combinatorially.