Williams, Lauren2009-02-231996Williams, Lauren K. 1996. Enumerating up-side self-avoiding walks on integer lattices. Electronic Journal of Combinatorics 3(1): #R31.1097-14401077-8926http://nrs.harvard.edu/urn-3:HUL.InstRepos:2624680A 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.en-US