The Nile on eBay FREE SHIPPING UK WIDE Polygons, Polyominoes and Polycubes by A.J. Guttmann
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn't been solved.
FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn't been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.
Back Cover
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
History and Introduction to Polygon Models and Polyominoes.- Lattice Polygons and Related Objects.- Exactly Solved Models.- Why Are So Many Problems Unsolved?.- The Anisotropic Generating Function of Self-Avoiding Polygons is not D-Finite.- Polygons and the Lace Expansion.- Exact Enumerations.- Series Analysis.- Monte Carlo Methods for Lattice Polygons.- Effect of Confinement: Polygons in Strips, Slabs and Rectangles.- Limit Distributions and Scaling Functions.- Interacting Lattice Polygons.- Fully Packed Loop Models on Finite Geometries.- Conformal Field Theory Applied to Loop Models.- Stochastic Lowner Evolution and the Scaling Limit of Critical Models.- Appendix: Series Data and Growth Constant, Amplitude and Exponent Estimates.
Long Description
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn't been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf'c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.
Feature
The only 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
Details ISBN9401777128 Short Title POLYGONS POLYOMINOES & POLYCUB Publisher Springer Series Lecture Notes in Physics Language English ISBN-10 9401777128 ISBN-13 9789401777124 Media Book Format Paperback DEWEY 576.15 Series Number 775 Author A.J. Guttmann Year 2016 Imprint Springer Place of Publication Dordrecht Country of Publication Netherlands Edited by A. J. Guttmann Publication Date 2016-08-23 UK Release Date 2016-08-23 Illustrations XIX, 490 p. Pages 490 Alternative 9781402099267 Audience Professional & Vocational Edition Description Softcover Reprint of the Original 1st 2009 ed. We've got this
At The Nile, if you're looking for it, we've got it.With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love!
30 DAY RETURN POLICY
No questions asked, 30 day returns!
FREE DELIVERY
No matter where you are in the UK, delivery is free.
SECURE PAYMENT
Peace of mind by paying through PayPal and eBay Buyer Protection TheNile_Item_ID:137855790;
Your request is processing... Please Wait