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)

• 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.

“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) ​

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)

• 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.

“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) ​

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)

• 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.

“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) ​