Proofs and Confirmations
The Story of the Alternating-Sign Matrix Conjecture
By (author) David M. Bressoud
Series edited by William Watkins Gerald L. Alexanderson
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Proofs and Confirmations by David M. Bressoud
Book DescriptionThis is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.
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Book DetailsISBN: 9780521666466
(228mm x 152mm x 17mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 13-Aug-1999
Country of Publication: United Kingdom
Books By Author David M. Bressoud
Radical Approach to Lebesgue's Theory of Integration, Hardback (January 2008)» View all books by David M. Bressoud
An introduction to measure theory and Lebesgue integration rooted in the historical questions that led to its development.
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