Extensions and generalizations of geometric bijections for graphs

Algebra Seminar
Monday, September 12, 2022 - 1:30pm for 1 hour (actually 50 minutes)
Clough 125 Classroom
Changxin Ding – Georgia Institute of Technology – cding66@gatech.eduhttps://sites.google.com/brandeis.edu/dingchangxin/home
Papri Dey

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.