Counting equivalence classes of vertex pairs modulo the dihedral action on the associahedron

摘要

This paper proves explicit formulae for the number of edges, 2-sets and diagonals in the associahedron of dimension n modulo the action of the dihedral group. A generating function for the number of k-sets modulo this action, as well as a formula for the cycle index, is given. A table of values is also provided.