Exact solution of two classes of prudent polygons
Combinatorics
2010-01-26 v3
Abstract
Prudent 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.
Keywords
Cite
@article{arxiv.0809.5232,
title = {Exact solution of two classes of prudent polygons},
author = {Uwe Schwerdtfeger},
journal= {arXiv preprint arXiv:0809.5232},
year = {2010}
}
Comments
11 pages, 3 figures; 14 pages, 4 figures, improved exposition, additional figure; 23 pages, 12 figures, additional section and figures