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History and Introduction to Polygon Models and Polyominoes

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Book cover Polygons, Polyominoes and Polycubes

Part of the book series: Lecture Notes in Physics ((LNP,volume 775))

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-dimensional square lattice Z2, or its three-dimensional counterpart, Z3, called the simple-cubic (sc) lattice, or its higher dimensional analogue Zd, called the (d-dimensional) hyper-cubic lattice. Other two-dimensional lattices, such as the triangular (t) and hexagonal (h) lattices, and other three-dimensional lattices, such as the body-centred cubic (bcc), face-centred cubic (fcc) and tetrahedral or diamond (d) lattices will also be mentioned.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Melbourne, Victoria, Australia

    Anthony J Guttmann

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  1. Anthony J Guttmann
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Editors and Affiliations

  1. Department of Mathematics and Statistics, The University of Melbourne, Victoria, 3010, Australia

    Anthony J. Guttman

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Guttmann, A.J. (2009). History and Introduction to Polygon Models and Polyominoes. In: Guttman, A.J. (eds) Polygons, Polyominoes and Polycubes. Lecture Notes in Physics, vol 775. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9927-4_1

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