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The perimeter generating function of punctured staircase polygons

Anthony J Guttmann and Iwan Jensen

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Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of punctured staircase polygons (staircase polygons with a single internal staircase hole). We find that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We perform an analysis of the properties of the differential equation.


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

02.30.Mv Approximations and expansions

02.30.Hq Ordinary differential equations

02.10.Ox Combinatorics; graph theory

02.10.Yn Matrix theory

MSC

05Exx Algebraic combinatorics

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

11C20 Matrices, determinants (See also 15A36)

51E12 Generalized quadrangles, generalized polygons

05A15 Exact enumeration problems, generating functions (See also 33Cxx, 33Dxx)

68R05 Combinatorics

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 15 (14 April 2006)

Received 15 December 2005

Published 29 March 2006



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