Anthony J Guttmann and Iwan Jensen 2006 J. Phys. A: Math. Gen. 39 3871 doi:10.1088/0305-4470/39/15/002
Anthony J Guttmann and Iwan Jensen
Show affiliationsUsing 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.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.30.Mv Approximations and expansions
02.30.Hq Ordinary differential equations
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)
Issue 15 (14 April 2006)
Received 15 December 2005
Published 29 March 2006
Anthony J Guttmann and Iwan Jensen 2006 J. Phys. A: Math. Gen. 39 3871
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