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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Polygons, Polyominoes and Polycubes (Paperback, Softcover reprint of the original 1st ed. 2009)
Loot Price: R1,585
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Polygons, Polyominoes and Polycubes (Paperback, Softcover reprint of the original 1st ed. 2009)
Series: Lecture Notes in Physics, 775
Expected to ship within 10 - 15 working days
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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.
General
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