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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.

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This 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 counting formula conjectured in the late 1970s. Researchers drawn to this problem began making connections to disparate topics in mathematics and physics including partition theory, symmetric functions, hypergeometric series, and statistical mechanics.The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do, and even researchers in combinatorics will find something new here.

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ISBN 10: 0521666465
ISBN 13: 9780521666466

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**Book Description **Cambridge University Press. Paperback. Book Condition: new. BRAND NEW PRINT ON DEMAND., Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture, David M. Bressoud, William Watkins, Gerald L. Alexanderson, Dipa Choudhury, William J. Firey, This 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. Bookseller Inventory # B9780521666466

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CAMBRIDGE UNIVERSITY PRESS, United Kingdom
(2011)

ISBN 10: 0521666465
ISBN 13: 9780521666466

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**Book Description **CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2011. Paperback. Book Condition: New. New.. 221 x 150 mm. Language: English Brand New Book ***** Print on Demand *****. This 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. Bookseller Inventory # AAV9780521666466

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Published by
Cambridge University Press
(1999)

ISBN 10: 0521666465
ISBN 13: 9780521666466

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**Book Description **Cambridge University Press, 1999. PAP. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # I2-9780521666466

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Published by
CAMBRIDGE UNIVERSITY PRESS, United Kingdom
(1999)

ISBN 10: 0521666465
ISBN 13: 9780521666466

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Quantity Available: 10

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**Book Description **CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1999. Paperback. Book Condition: New. New.. 221 x 150 mm. Language: English Brand New Book ***** Print on Demand *****.This 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. Bookseller Inventory # AAV9780521666466

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Published by
Cambridge University Press
(1999)

ISBN 10: 0521666465
ISBN 13: 9780521666466

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**Book Description **Cambridge University Press, 1999. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: An introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. Bookseller Inventory # ABE_book_new_0521666465

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Published by
Cambridge University Press
(1999)

ISBN 10: 0521666465
ISBN 13: 9780521666466

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**Book Description **Cambridge University Press, 1999. Paperback. Book Condition: New. book. Bookseller Inventory # 0521666465

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ISBN 10: 0521666465
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**Book Description **Book Condition: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Bookseller Inventory # NU-ING-00307705

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Published by
Cambridge University Press
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ISBN 13: 9780521666466

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**Book Description **Cambridge University Press, 1999. PAP. Book Condition: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # LQ-9780521666466

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**Book Description **1999. Paperback. Book Condition: NEW. 9780521666466 Paperback, 292pp., This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # 469016

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Published by
The Mathematical Association of America
(1999)

ISBN 10: 0521666465
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**Book Description **The Mathematical Association of America, 1999. Paperback. Book Condition: New. Bookseller Inventory # DADAX0521666465

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