Fr. 169.00

Combinatorics and Complexity of Partition Functions

Anglais · Livre de poche

Expédition généralement dans un délai de 6 à 7 semaines

Description

En savoir plus

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial  structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. 
The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. 

Table des matières

Chapter I. Introduction.- Chapter II. Preliminaries.- Chapter III. Permanents.- Chapter IV. Hafnians and Multidimensional Permanents.- Chapter V. The Matching Polynomial.- Chapter VI. The Independence Polynomial.- Chapter VII. The Graph Homomorphism Partition Function.- Chapter VIII. Partition Functions of Integer Flows.- References.- Index.

A propos de l'auteur

Alexander Barvinok is a professor of mathematics at the University of Michigan in Ann Arbor, interested in computational complexity and algorithms in algebra, geometry and combinatorics. The reader might be familiar with his books “A Course in Convexity” (AMS, 2002) and “Integer Points in Polyhedra” (EMS, 2008)

Résumé

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial  structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. 
The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. 

Texte suppl.

“The book is aimed at graduate students and researchers in theoretical computer science, combinatorics and statistical physics. … The author has the ability to make complicated proofs very accessible while not sacrificing any mathematical rigour, making it a pleasure to read. … The book also moves from the particular to the general … . An advantage of this is that it makes it easier to understand the key ideas.” (Guus Regts, Mathematical Reviews, August, 2018)

Commentaire

"The book is aimed at graduate students and researchers in theoretical computer science, combinatorics and statistical physics. ... The author has the ability to make complicated proofs very accessible while not sacrificing any mathematical rigour, making it a pleasure to read. ... The book also moves from the particular to the general ... . An advantage of this is that it makes it easier to understand the key ideas." (Guus Regts, Mathematical Reviews, August, 2018)

Commentaires des clients

Aucune analyse n'a été rédigée sur cet article pour le moment. Sois le premier à donner ton avis et aide les autres utilisateurs à prendre leur décision d'achat.

Écris un commentaire

Super ou nul ? Donne ton propre avis.

Pour les messages à CeDe.ch, veuillez utiliser le formulaire de contact.

Il faut impérativement remplir les champs de saisie marqués d'une *.

En soumettant ce formulaire, tu acceptes notre déclaration de protection des données.