A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Enumeration
Haruspicy 2: the anisotropic generating function of self-avoiding polygons is not D-finite
Journal of Combinatorial Theory Series A
Polynomial equations with one catalytic variable, algebraic series and map enumeration
Journal of Combinatorial Theory Series B
Two non-holonomic lattice walks in the quarter plane
Theoretical Computer Science
The enumeration of prudent polygons by area and its unusual asymptotics
Journal of Combinatorial Theory Series A
Some New Self-avoiding Walk and Polygon Models
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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Prudent walks are self-avoiding walks on a 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 of the walk is adjacent to its first one. More precisely, we give the half-perimeter generating functions of two subclasses of prudent polygons on the square lattice, which turn out to be algebraic and non-D-finite, respectively.