Counting Lattice Paths and Walks with Several Step Vectors

摘要

Many famous researchers in computer science, mathematics and other areas have studied enumerative problems in lattice path and walks which could be applied to many fields. We will discuss some new enumerative problems including some pattern avoidance problems in lattice paths and walks with several step vectors. Results on stretches and turns are presented and several open problems are posted. A few approaches are used in this paper such as computational, generating function, closed formula and constructional method. You will observe many interesting integer sequences as well.