Sampling and Counting 3-orientations of Planar

  title={Sampling and Counting 3-orientations of Planar},
  author={Sarah Miracle and Dana Randall and Amanda Pascoe Streib and Prasad Tetali},
Given a planar triangulation, a 3-orientation is an orientation of the internal edges so all internal vertices have out-degree three. Each 3-orientation gives rise to a unique edge coloring known as a Schnyder wood that has proven powerful for various computing and combinatorics applications. We consider natural Markov chains for sampling uniformly from the set of 3-orientations. First, we study a “triangle-reversing” chain on the space of 3-orientations of a fixed triangulation that reverses… CONTINUE READING