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020 _a9781402099274
_9978-1-4020-9927-4
024 7 _a10.1007/978-1-4020-9927-4
_2doi
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072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.15
_223
245 1 0 _aPolygons, Polyominoes and Polycubes
_h[electronic resource] /
_cedited by Anthony J. Guttman.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2009.
300 _aXIX, 490 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v775
505 0 _aHistory 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.
520 _aThis 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.
650 0 _aMathematical physics.
650 0 _aAlgorithms.
650 0 _aElectronic data processing.
650 0 _aCombinatorics.
650 0 _aChemistry
_xMathematics.
650 1 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aAlgorithms.
_0http://scigraph.springernature.com/things/product-market-codes/M14018
650 2 4 _aNumeric Computing.
_0http://scigraph.springernature.com/things/product-market-codes/I1701X
650 2 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aMath. Applications in Chemistry.
_0http://scigraph.springernature.com/things/product-market-codes/C17004
700 1 _aGuttman, Anthony J.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781402099953
776 0 8 _iPrinted edition:
_z9781402099267
776 0 8 _iPrinted edition:
_z9789401777124
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v775
856 4 0 _uhttps://doi.org/10.1007/978-1-4020-9927-4
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