Area limit laws for symmetry classes of staircase polygons

Authors:
U. Schwerdtfeger;C. Richard;B. Thatte
Affiliations:
Fakultät für mathematik, universität bielefeld, postfach 10 01 31, 33501 bielefeld, germany (e-mail: uschwerd@math.uni-bielefeld.de);Department für mathematik, universität erlangen–nürnberg, bismarckstraße 1 1/2, 91054 erlangen, germany (e-mail: richard@mi.uni-erlangen.de);Mathematics and computer science building, university of canterbury, private bag 40800, christchurch, new zealand (e-mail: b.thatte@math.canterbury.ac.nz)
Venue:
Combinatorics, Probability and Computing
Year:
2010

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Abstract

We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with the same probability. This complements a previous study by Leroux and Rassart, where explicit expressions for the area and perimeter generating functions of these classes have been derived.