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Area Limit Laws for Symmetry Classes of Staircase Polygons

Published online by Cambridge University Press:  27 January 2010

U. SCHWERDTFEGER ,
C. RICHARD  and
B. THATTE
U. SCHWERDTFEGER
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany (e-mail: uschwerd@math.uni-bielefeld.de)
C. RICHARD
Affiliation:
Department für Mathematik, Universität Erlangen–Nürnberg, Bismarckstraße 1 1/2, 91054 Erlangen, Germany (e-mail: richard@mi.uni-erlangen.de)
B. THATTE
Affiliation:
Mathematics and Computer Science Building, University of Canterbury, Private Bag 40800, Christchurch, New Zealand (e-mail: b.thatte@math.canterbury.ac.nz)
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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 3 , May 2010 , pp. 441 - 461
Copyright
Copyright © Cambridge University Press 2010

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