2021-12-232021-12-2319784237714https://hdl.handle.net/10657/8434A new method is presented for the construction and analysis of non self-intersecting random walks which: (a) makes economic use of digital computer time, both in the exact enumeration of walks and in applying Monte-Carlo methods; and (b) appears to provide a sympathetic environment for analytical investigations such as obtaining the upper bound for the number of paths on a grid. An algorithm for the enumeration of elementary paths on a rectangular grid is presented and discussed; a program based on this algorithm is exhibited. This program was written for a square, n x n, grid and results are given for n = 2, 3, 4, and 5.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital