Book Chapter

History and Introduction to Polygon Models and Polyominoes

Anthony J Guttmann

POLYGONS, POLYOMINOES AND POLYCUBES | Lecture Notes in Physics | SPRINGER-VERLAG BERLIN | Published : 2009

Abstract

In this book we will primarily be concerned with the properties and applications of self-avoiding polygons (SAP). Two closely related problems are those of polyomi-noes, and the much broader one of tilings. We will describe and discuss polyominoes and, in the context of a discussion of SAP, will briefly mention relevant aspects of the subject of tilings. In passing we will also concern ourselves with a discussion of some properties of polycubes. It will also turn out to be appropriate to discuss self-avoiding walks (SAW), as SAP can be usefully and simply related to a proper subset of SAW. In all cases we shall be considering paths on a regular lattice. This will most often be the two-dimens..

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University of Melbourne Researchers