The perimeter generating functions of three-choice, imperfect, and one-punctured staircase polygons
The perimeter generating functions of three-choice, imperfect, and one-punctured staircase polygons
We consider the isotropic perimeter generating functions of three-choice, imperfect, and 1-punctured staircase polygons, whose 8th order linear Fuchsian ODEs are previously known. We derive simple relationships between the three generating functions, and show that all three generating functions are joint solutions of a common 12th order Fuchsian linear ODE. …