| 书目名称 | Polygons, Polyominoes and Polycubes | | 编辑 | Anthony J. Guttman | | 视频video | | | 概述 | 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 | | 丛书名称 | Lecture Notes in Physics | | 图书封面 |  | | 描述 | 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 bee | | 出版日期 | Book 20091st edition | | 关键词 | Counting; Lattice; Mathematica; Monte Carlo method; Theoretical physics; algorithms; biology; calculus; comp | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4020-9927-4 | | isbn_softcover | 978-94-017-7712-4 | | isbn_ebook | 978-1-4020-9927-4Series ISSN 0075-8450 Series E-ISSN 1616-6361 | | issn_series | 0075-8450 | | copyright | Springer Science+Business Media B.V. 2009 |
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发表于 2025-3-21 17:41:52
