A New Face Iterator for Polyhedra and for More General Finite Locally Branched Lattices

Abstract We discuss a new memory-efficient depth-first algorithm and its implementation that iterates over all elements of finite locally branched lattice. This can be applied to face lattices polyhedra various generalizations such as polyhedral complexes subdivisions manifolds, extended tight spans closed sets matroids. Its practical is very fast compared state-of-the-art implementations previously considered algorithms. Based on recent work Bruns, García-Sánchez, O’Neill, Wilburne, we apply this prove Wilf’s conjecture for numerical semigroups multiplicity 19 by iterating through the faces Kunz cone identifying possible bad then checking these do not yield counterexamples conjecture.