Permanents / Henryk Minc ; with a foreword by Marvin Marcus.

Format:

Book

Author/Creator:

Minc, Henryk, author.

Contributor:

Marcus, Marvin, 1927- writer of foreword.

Series:

Encyclopedia of mathematics and its applications ; v. 6.

Encyclopedia of mathematics and its applications ; volume 6

Language:

English

Subjects (All):

Permanents (Matrices).

Inequalities (Mathematics).

Physical Description:

1 online resource (xviii, 205 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1984.

Language Note:

English

Summary:

The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Contents:

Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; CHAPTER 1 The Theory of Permanents in the Historical Order of Development; 1.1 Introduction; 1.2 The Originators: Binet and Cauchy; 1.3 The Continuators: Borchardt, Cayley, and the Master from Edinburgh-Sir Thomas Muir; 1.4 Renaissance of Permanents: Muirhead's Theorem, Pοĺya's Problem, Schur's Inequality, and van der Waerden's Conjecture; 1.5 The New Era: Marvin Marcus and Company; Problems; CHAPTER 2 Properties of Permanents; 2.1 Elementary Properties

2.2 The Permanent Function as an Inner ProductProblems; CHAPTER 3 (0, 1)-Matrices; 3.1 Incidence Matrices; 3.2 Theorems of Frobenius and Konig; 3.3 Structure of Square (0, 1)-Matrices; 3.4 (0, 1)-Circulants; Problems; CHAPTER 4 Lower Bounds for Permanents; 4.1 Marshall Hall's Theorem; 4.2 (0, I)-Matrices; 4.3 Fully Indecomposable (0, I)-Matrices; 4.4 Nonnegative Matrices; 4.5 Positive Semi-definite Hermitian Matrices; Problems; CHAPTER 5 The van der Waerden Conjecture; 5.1 The Marcus-Newman Theory; 5.2 Properties of Minimizing Matrices; 5.3 Some Partial Results. Friedland's Theorem

5.4 A Conjecture of Marcus and Mine5.5 Lower Bounds for the Permanents of Doubly Stochastic Matrices; Problems; CHAPTER 6 Upper Bounds for Permanents; 6.1 From Muir to Jurkat and Ryser; 6.2 (0, I)-Matrices; 6.3 Nonnegative Matrices; 6.4 Complex Matrices; Problems; CHAPTER 7 Evaluation of Permanents; 7.1 Binet-Mine Method; 7.2 Ryser's Method; 7.3 Comparison of Evaluation Methods; Problems; CHAPTER 8 More about Permanents; 8.1 Other Results; 8.2 Some Applications of Permanents; 8.3 Conjectures and Unsolved Problems-Vintage 1965; 8.4 Conjectures and Unsolved Problems-A Current List; Problems

BibliographyIndex to Bibliography; Index of Notation; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Bibliography: p. 161-196.

ISBN:

1-139-88163-9

1-107-26425-1

1-107-26674-2

1-107-26317-4

1-107-26981-4

1-107-34068-3