Combinatorics and Complexity of Partition Functions

  • Alexander Barvinok

Part of the Algorithms and Combinatorics book series (AC, volume 30)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Alexander Barvinok
    Pages 1-7
  3. Alexander Barvinok
    Pages 9-45
  4. Alexander Barvinok
    Pages 47-92
  5. Alexander Barvinok
    Pages 93-143
  6. Alexander Barvinok
    Pages 145-179
  7. Alexander Barvinok
    Pages 181-227
  8. Alexander Barvinok
    Pages 229-267
  9. Alexander Barvinok
    Pages 269-292
  10. Back Matter
    Pages 293-303

About this book


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. 


algorithms complexity partition function permanent mathing polynomial independence polynomial graph homomorphism integer flow stable polynomials correlation decay interpolation scaling

Authors and affiliations

  • Alexander Barvinok
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn Arbor, MIUSA

Bibliographic information