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Extensions and generalizations of geometric bijections for graphs

Algebra & Discrete Mathematics

Speaker: Changxin Ding, Georgia Tech
Location: Zoom
Start time: Fri, Oct 7 2022, 3:10PM

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.

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