Cambrian triangulations and their tropical realizations

Abstract

This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on ν-Tamari lattices and their tropical realizations. For any signature ε ∈ {±} n , we consider a family of ε-trees in bijection with the triangulations of the ε-polygon. These ε-trees define a flag regular triangulation T ε of the subpolytope conv {(e i•