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010   $a3-319-51829-1
024 7 $a10.1007/978-3-319-51829-9
035   $a(CKB)3710000001100884
035   $a(MiAaPQ)EBC4822606
035   $a(DE-He213)978-3-319-51829-9
035   $a(PPN)199767467
035   $a(MiAaPQ)EBC6237365
035   $a(EXLCZ)993710000001100884
100   $a20170314d2016      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aCombinatorics and Complexity of Partition Functions /$fby Alexander Barvinok
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (304 pages) $cillustrations
225 1 $aAlgorithms and Combinatorics,$x0937-5511 ;$v30
311 08$a3-319-51828-3 
320   $aIncludes bibliographical references and index.
327   $aChapter 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.
330   $aPartition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. .
410  0$aAlgorithms and Combinatorics,$x0937-5511 ;$v30
606   $aAlgorithms
606   $aCombinatorial analysis
606   $aComputer science?Mathematics
606   $aStatistical physics
606   $aDynamics
606   $aApproximation theory
606   $aMathematics of Algorithmic Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/M13130
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
606   $aDiscrete Mathematics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17028
606   $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000
606   $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018
606   $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023
615  0$aAlgorithms.
615  0$aCombinatorial analysis.
615  0$aComputer science?Mathematics.
615  0$aStatistical physics.
615  0$aDynamics.
615  0$aApproximation theory.
615 14$aMathematics of Algorithmic Complexity.
615 24$aCombinatorics.
615 24$aDiscrete Mathematics in Computer Science.
615 24$aComplex Systems.
615 24$aAlgorithms.
615 24$aApproximations and Expansions.
676   $a510
700   $aBarvinok$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut$0322075
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254078803321
996   $aCombinatorics and complexity of partition functions$91523225
997   $aUNINA