Haruspicy 2: the anisotropic generating function of self-avoiding polygons is not D-finite

Authors:
Andrew Rechnitzer
Affiliations:
Department of Mathematics and Statistics, The University of Melbourne, Parkville Victoria, Australia
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

Citing 6
Cited 2

Enumerative combinatorics

Enumerative combinatorics
A method for the enumeration of various classes of column-convex polygons

Discrete Mathematics
Indicators of solvability for lattice models

Discrete Mathematics
Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings

Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Haruspicy and anisotropic generating functions

Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
The site-perimeter of bargraphs

Advances in Applied Mathematics

Two non-holonomic lattice walks in the quarter plane

Theoretical Computer Science
Exact solution of two classes of prudent polygons

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that the anisotropic generating function of self-avoiding polygons is not a D-finite function--proving a conjecture of Guttmann [Discrete Math. 217 (2000) 167-189] and Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344-347]. This result is also generalised to self-avoiding polygons on hypercubic lattices. Using the haruspicy techniques developed in an earlier paper [Rechnitzer, Adv. Appl. Math. 30 (2003) 228-257], we are also able to prove the form of the coefficients of the anisotropic generating function, which was first conjectured in Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344-347].