The perimeter generating function of punctured staircase polygons

Abstract

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.

14 pages, 2 figures, IOP style

References in corpus (5)

• The Fuchsian differential equation of the square lattice Ising model $\chi (3)$ susceptibility
• Square lattice Ising model susceptibility: Series expansion method and differential equation for ${\chi }^{(3)}$
• Punctured polygons and polyominoes on the square lattice
• Ising model susceptibility: Fuchsian differential equation for ${\chi }^{(4)}$ and its factorization properties
• Fuchsian differential equation for the perimeter generating function of three-choice polygons

Cited by in corpus (7)

• Difference system for Selberg correlation integrals
• Square lattice self-avoiding walks and biased differential approximants
• Exact perimeter generating function for a model of punctured staircase polygons
• The perimeter generating functions of three-choice, imperfect, and 1-punctured staircase polygons
• Area distribution and scaling function for punctured polygons
• The Half-Perimeter Generating Function of Gated and Wicketed Ferrers diagrams
• Limit distributions and scaling functions