This page distributes computational resources for the paper "Markov degree of Birkhoff model" by Yamaguchi, Ogawa and Takemura, concerning the (n,r)-Birkhoff model for r less than or equal to 5.

Two zip files are provided.

dotfiles.zip contains files "graph(r=i)" (i=1,2,...). In these files, in DOT language, we provide information on connected graphs which have i vertices. Three candidates are written in all vertices and we connect the vertices which have common candidates. All candidates are at most three. These graphs correspond to the representatives when we define equivalence class of sufficient statistics from the symmetry of rank and candidates.

epsfiles.zip contains files "fiber_and_graph(r=i)" (i=1,2,...), which are eps graphic files. In these files we provide graphs of the sufficient statistics and their fibers. A rectangle corresponds to a vote and a group of three rectangles corresponds to the one of the elements of the fiber. Same rectangles are connected.