Cross‐ratio degrees and triangulations

Abstract The cross‐ratio degree problem counts configurations of points on with prescribed cross‐ratios. Cross‐ratio degrees arise in many corners of combinatorics and geometry, but their structure is not well‐understood in general. Interestingly, examining various special cases of the problem can yield combinatorial structures that are both diverse and rich. In this paper, we prove a simple closed formula for a class of cross‐ratio degrees indexed by triangulations of an ‐gon; these degrees are connected to the geometry of the real locus of , and to positive geometry.