In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each ...
The nth crossing number of a graph G, denoted crn(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a > b &g...
Extending a bijection recently introduced by Poulalhon and Schaeffer [15] for triangulations of the sphere we design an efficient algorithm for encoding (topological) triangulatio...