Self-avoiding walks

A self avoiding walk is a path through a graph where no vertex is visited more than once. One problem is to consider the cartesian lattice, and the paths from \((0,0)\) to \((m,n)\). If we only allow paths in the &ldquo;positive direction&rdquo;, so that from \((i,j)\) the path can only proceed to \((i+1,j)\) or \((i,j+1)\) we have what are sometimes called &ldquo;staircase paths&rdquo;: The…