Proofs and Confirmations

The Story of the Alternating-Sign Matrix Conjecture

David M. Bressoud (Macalester College, Minnesota), William Watkins, Gerald L. Alexanderson , Dipa Choudhury

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English

Cambridge University Press
27 December 1999

Mathematics & Sciences; Mathematical logic; Combinatorics & graph theory

Series: Spectrum

This introduction to recent developments in algebraic combinatorics illustrates how research in mathematics actually progresses.

The author recounts the dramatic search for and discovery of a proof of a counting formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices.

While it was apparent that the conjecture must be true, the proof was elusive. As a result, researchers became drawn to this problem and made connections to aspects of the invariant theory of Jacobi, Sylvester, Cayley, MacMahon, Schur, and Young; to partitions and plane partitions; to symmetric functions; to hypergeometric and basic hypergeometric series; and, finally, to the six-vertex model of statistical mechanics. This volume is accessible to anyone with a knowledge of linear algebra, and it includes extensive exercises and Mathematica programs to help facilitate personal exploration. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something unique within Proofs and Confirmations.

By: David M. Bressoud (Macalester College Minnesota)
Series edited by: William Watkins, Gerald L. Alexanderson, Dipa Choudhury, William J. Firey
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 17mm
Weight: 430g
ISBN: 9780521666466
ISBN 10: 0521666465
Series: Spectrum
Pages: 292
Publication Date: 27 December 1999
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture

'Proofs and Confirmations is one of the most brilliant examples of mathematical exposition that I have encountered, in many years of reading the same. This is not for the faint-hearted, nor is Proofs and Confirmations a book that can be read in an easy chair, like a novel; it demands active participation by the reader. But Bressoud rewards such readers with a panorama of combinatorics today and with renewed awe at the human ability to penetrate the deeply hidden mysteries of pure mathematics.' Herbert S. Wilf, Science 'The unexpected twists and turns will hardly be matched in any novel - this book allows us all to share in the excitement ... a brilliant book.' Alun O. Morris 'I strongly recommend the book as an account of a remarkable mathematical development.' P. J. Cameron, Proceedings of the Edinburgh Mathematical Society 'This is an excellent book which can be recommended without hesitation, not only to specialists in the field, but to any mathematician with time to read something interesting and nicely written.' EMS