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Author: Adrian Tanasa
Publisher: Oxford University Press
Published: 2021
Total Pages: 409
ISBN-13: 0192895494
DOWNLOAD EBOOKThe goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Author: V.A. Malyshev
Publisher: Springer Science & Business Media
Published: 2002-08-31
Total Pages: 352
ISBN-13: 9781402007927
DOWNLOAD EBOOKNew and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Author: Kurusch Ebrahimi-Fard
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 480
ISBN-13: 0821853295
DOWNLOAD EBOOKThis book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.
Author: Jean-Pierre Gazeau
Publisher: IOS Press
Published: 2007
Total Pages: 349
ISBN-13: 1586037064
DOWNLOAD EBOOKAims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.
Author: Karen Yeats
Publisher: Springer
Published: 2016-11-23
Total Pages: 120
ISBN-13: 3319475517
DOWNLOAD EBOOKThis book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
Author: George E. Andrews
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 144
ISBN-13: 0821807161
DOWNLOAD EBOOKIntegrates developments and related applications in $q$-series with a historical development of the field. This book develops important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory.
Author: Marc Mézard
Publisher: Oxford University Press
Published: 2009-01-22
Total Pages: 584
ISBN-13: 019857083X
DOWNLOAD EBOOKA very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.
Author: Douglas B. West
Publisher: Cambridge University Press
Published: 2021
Total Pages: 990
ISBN-13: 1107058589
DOWNLOAD EBOOKThis is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.
Author: Philippe Flajolet
Publisher: Cambridge University Press
Published: 2009-01-15
Total Pages: 825
ISBN-13: 1139477161
DOWNLOAD EBOOKAnalytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: Sriram Pemmaraju
Publisher: Cambridge University Press
Published: 2009-10-15
Total Pages: 615
ISBN-13: 1107268710
DOWNLOAD EBOOKThis book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.
