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Combinatorics and Complexity of Partition Functions: Algorithms and Applications

John Dos Passos

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

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

by Alexander Barvinok

4.8 out of 5

Language	:	English
File size	:	6494 KB
Screen Reader	:	Supported
Print length	:	309 pages

Partition functions are ubiquitous in mathematics and computer science. They arise in a wide variety of applications, including combinatorics, number theory, and statistical physics. The combinatorics of partition functions deals with the number of ways to partition a set into a given number of subsets. The complexity of partition function algorithms deals with the computational complexity of finding the number of ways to partition a set into a given number of subsets.

This book provides a comprehensive to the combinatorics and complexity of partition functions. The book is divided into two parts. The first part covers the basic theory of partition functions. The second part covers the asymptotics of partition functions and the complexity of partition function algorithms.

Part I: Basic Theory of Partition Functions

The first part of the book covers the basic theory of partition functions. This part of the book provides a foundation for the rest of the book. The chapters in this part of the book cover the following topics:

* The definition of a partition function * The generating function for the number of partitions of a set * The asymptotic behavior of the number of partitions of a set * The complexity of partition function algorithms

Part II: Asymptotics of Partition Functions and Complexity of Partition Function Algorithms

The second part of the book covers the asymptotics of partition functions and the complexity of partition function algorithms. This part of the book builds on the foundation provided in the first part of the book. The chapters in this part of the book cover the following topics:

* The asymptotic behavior of the number of partitions of a set * The complexity of partition function algorithms * Applications of partition functions

This book provides a comprehensive to the combinatorics and complexity of partition functions. The book is suitable for graduate students and researchers in mathematics and computer science.

About the Author

Dr. Richard Stanley is a professor of mathematics at the Massachusetts Institute of Technology. He is a leading expert in combinatorics and has written several books on the subject.