Combinatorics and Complexity of Partition Functions (Algorithms and Combinatorics, 30)

Barvinok, Alexander

ISBN 10: 3319847511 / ISBN 13: 9783319847511

Editore: Springer, 2018

In. Codice articolo ria9783319847511_new

Riassunto:

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. 

Informazioni sull?autore:

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)

Dati bibliografici

Titolo: Combinatorics and Complexity of Partition ...
Casa editrice: Springer
Data di pubblicazione: 2018
Legatura: Brossura
Condizione: New