Enumerating up-side self-avoiding walks on integer lattices
Summary: A self-avoiding walk (saw) is a path on a lattice that does not pass through the same point twice. Though mathematicians have studied saws for over fifty years, the number of \(n\)-step saws is unknown. This paper examines a special case of this problem, finding the number of \(n\)-step ``up-side'' saws (ussaws), saws restricted to moving up and sideways. It presents formulas for the number of \(n\)-step ussaws on various lattices, found using generating functions with decomposition and recursive methods.
scientific article; zbMATH DE number 1120245