The Anisotropic Generating Function of Self-Avoiding Polygons is not D-Finite

DOI10.1007/978-1-4020-9927-4_5zbMath1180.82088OpenAlexW1566262162MaRDI QIDQ3651682

Andrew Rechnitzer

Publication date: 11 December 2009

Published in: Polygons, Polyominoes and Polycubes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4020-9927-4_5

zbMATH Keywords

self-avoiding polygonslattice animalsenumerative combinatorics

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Polyominoes (05B50)

Related Items (2)

Polycubes with small perimeter defect ⋮ Synergistic development of differential approximants and the finite lattice method in lattice statistics

Cites Work

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• The enumeration of permutations with a prescribed number of ``forbidden patterns
• D-finite power series
• Inversion relations, reciprocity and polyominoes
• Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings
• Haruspicy and anisotropic generating functions
• The site-perimeter of bargraphs
• Lattice animals and heaps of dimers
• A method for the enumeration of various classes of column-convex polygons
• Haruspicy 2: The anisotropic generating function of self-avoiding polygons is not D-finite
• Haruspicy 3: The anisotropic generating function of directed bond-animals is not D-finite
• Combinatorial Problems Suggested by the Statistical Mechanics of Domains and of Rubber-Like Molecules
• GFUN
• Solvability of Some Statistical Mechanical Systems
• Self-avoiding polygons on the square lattice

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