Lecture Notes in Physics

Polygons, Polyominoes and Polycubes

Editors: Guttmann, A. J. (Ed.)

  • The first book devoted to polygons
  • Presents a class of ultra-fast counting algorithms
  • New experimental mathematics techniques to conjecture exact solutions
  • Powerful mathematical tools to solve polygon problems
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eBook $109.00
price for USA (gross)
  • ISBN 978-1-4020-9927-4
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  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4020-9926-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems.

In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology and bio-informatics – can be expressed as counting problems, in which specified graphs, or shapes, are counted.

One very special class of shapes is that of polygons. These are closed, connected paths in space. We usually sketch them in two-dimensions, but they can exist in any dimension. The typical questions asked include "how many are there of a given perimeter?", "how big is the average polygon of given perimeter?", and corresponding questions about the area or volume enclosed. That is to say "how many enclosing a given area?" and "how large is an average polygon of given area?" Simple though these questions are to pose, they are extraordinarily difficult to answer. They are important questions because of the application of polygon, and the related problems of polyomino and polycube counting, to phenomena occurring in the natural world, and also because the study of these problems has been responsible for the development of powerful new techniques in mathematics and mathematical physics, as well as in computer science. These new techniques then find application more broadly.

The book brings together chapters from many of the major contributors in the field. An introductory chapter giving the history of the problem is followed by fourteen further chapters describing particular aspects of the problem, and applications to biology, to surface phenomena and to computer enumeration methods.

Table of contents (16 chapters)

  • History and Introduction to Polygon Models and Polyominoes

    Guttmann, Anthony J

    Pages 1-21

  • Lattice Polygons and Related Objects

    Whittington, Stuart G

    Pages 23-41

  • Exactly Solved Models

    Bousquet-Mélou, Mireille (et al.)

    Pages 43-78

  • Why Are So Many Problems Unsolved?

    Guttmann, Anthony J

    Pages 79-91

  • The Anisotropic Generating Function of Self-Avoiding Polygons is not D-Finite

    Rechnitzer, Andrew

    Pages 93-115

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4020-9927-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4020-9926-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Polygons, Polyominoes and Polycubes
Editors
  • A. J. Guttmann
Series Title
Lecture Notes in Physics
Series Volume
775
Copyright
2009
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-9927-4
DOI
10.1007/978-1-4020-9927-4
Hardcover ISBN
978-1-4020-9926-7
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XIX, 490
Additional Information
Jointly published with Canopus Academic Publishing Ltd.
Topics