Area limit laws for symmetry classes of staircase polygons

TL;DR

This paper establishes area limit laws for different symmetry classes of staircase polygons on the square lattice, expanding understanding of their probabilistic behavior within a uniform ensemble.

Contribution

It introduces new area limit laws for symmetry classes of staircase polygons, complementing prior explicit generating function results.

Findings

Derived area limit laws for symmetry classes

Extended previous explicit generating function results

Enhanced understanding of probabilistic properties of staircase polygons

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.