Unsolved Lattice Path Problems in Computational Science II
Shanzhen Gao, Keh-Hsun Chen · 2018
Lattice path enumeration and its applications have been studied by researchers in many areas such as computer science, mathematics, biology, physics, chemistry and statistics. They are related to number theory, geometry theory, combinatorics, graph theory, linear algebra and group theory. They are easy to state and understand although they are very difficult to be solved by researchers in mathematics or computer science. It seems to us that it is very challenging to find suitable mathematical methods or efficient algorithms to deal with them. This paper is the continuation of our previous paper, under the same title , which we refer to as Part I. In Part I: we discussed some enumerative problems on pattern avoidance in lattice paths, and many closed formulas, integer sequences, generating functions, and open problems were posted. In this paper, we will present the number of walks taking steps from various sets, such at {E,N,SW}, {W,S,NE}, ENW, and PSAWs, and closed formulas, integer sequences, generating functions, and open problems.