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

Rechnitzer, Andrew

doi:10.1007/978-1-4020-9927-4_5

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2017

2022

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Cited by 2 publications

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“…expressed in the title by Guttmann and Enting (1988c) turned to serious doubt (Guttmann and Enting 1996) with strong indications that polygon enumeration would not have a solution in terms of the 'standard' functions of mathematical physics. This led to a proof by Rechnitzer (2009) that the anisotropic polygon generating function was not D-finite.…”

Section: Discussionmentioning

confidence: 99%

Synergistic development of differential approximants and the finite lattice method in lattice statistics

Enting¹

2017

J. Phys. A: Math. Theor.

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Several decades of parallel developments in the calculation and analysis of series expansions for lattice statistics have led to many new insights into critical phenomena. These studies have centered on the use of the finite lattice method for series expansions in lattice statistics and the use of differential approximants in analysing such series. One of these strands of research ultimately led to the result that a number of unsolved lattice statistics problems cannot be expressed as D-finite functions. Somewhat ironically, given power and success of differential approximants in analysing series, neither the assumed functional form, nor any finite generalisation thereof can fit such cases exactly.

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Section: Discussionmentioning

confidence: 99%