Exact solution of two classes of prudent polygons

Details Exact solution of two classes of prudent polygons Exact solution of two classes of prudent polygons

2008-09-30

arxiv.org/abs/0809.5232v3

Mathematics

Combinatorics

11 pages, 3 figures; 14 pages, 4 figures, improved exposition, additional figure; 23 pages, 12 figures, additional section and

Scientific paper

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.

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