14 research outputs found
Exact solution of two classes of prudent polygons
Get PDFPrudent walks are self-avoiding walks on the square lattice which never step
into the direction of an already occupied vertex. We study the closed version
of these walks, called prudent polygons, where the last vertex is adjacent to
the first one. More precisely, we give the half-perimeter generating functions
of two subclasses of prudent polygons, which turn out to be algebraic and
non-D-finite, respectively.Comment: 11 pages, 3 figures; 14 pages, 4 figures, improved exposition,
additional figure; 23 pages, 12 figures, additional section and figure
