Polygons, Polyominoes and Polycubes

• Corporate Author: SpringerLink (Online service)
• Other Authors: Guttman, Anthony J. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2009.
• Series: Lecture Notes in Physics, 775
• Subjects: Physics.; Chemometrics.; Numerical analysis.; Algorithms.; Combinatorics.; Statistical physics.; Dynamical systems.; Mathematical Methods in Physics.; Numeric Computing.; Statistical Physics, Dynamical Systems and Complexity.; Math. Applications in Chemistry.

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 coun...

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.