Large Deviations of Convex Polyominoes

TL;DR

This paper establishes a large deviation principle for convex polyominoes, providing a theoretical framework to analyze their probabilistic behavior under various geometric constraints.

Contribution

It introduces a novel large deviation principle for convex polyominoes with fixed area and perimeter, advancing the mathematical understanding of their enumeration.

Findings

Large deviation principles derived for convex polyominoes.

Framework applicable under multiple geometric restrictions.

Enhances understanding of polyomino enumeration in probabilistic terms.

Abstract

Enumeration of various types of lattice polygons and in particular polyominoes is of primary importance in many machine learning, pattern recognition, and geometric analysis problems. In this work, we develop a large deviation principle for convex polyominoes under different restrictions, such as fixed area and/or perimeter.