The exact perimeter generating function for a model of punctured staircase polygons

Iwan Jensen, Andrew Rechnitzer

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We have derived the perimeter generating function of a model of punctured staircase polygons in which the internal staircase polygon is rotated by a 90° angle with respect to the outer staircase polygon. In one approach we calculated a long series expansion for the problem and found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 4. We then solved this ODE and found a closed form expression for the generating function. This is a highly unusual and most fortuitous result since ODEs of such high order very rarely permit a closed form solution. In a second approach we proved the result for the generating function exactly using combinatorial arguments. This latter solution allows many generalizations including models with other types of punctures and a model with any fixed number of nested rotated staircase punctures.

Original languageEnglish
Article number215002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number21
Publication statusPublished - 6 May 2008
Externally publishedYes


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