Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Spectrum)

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9780521666466: Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (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.

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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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Bressoud, David M.
Published by 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. 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 # AAZ9780521666466

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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. 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 # AAZ9780521666466

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Book Description Cambridge University Press, 1999. Book Condition: New. An introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. Series Editor(s): Watkins, William; Alexanderson, Gerald L.; Choudhury, Dipa; Firey, William J.; Kalman, Dan; Lang, Eleanor; Merris, Russell L.; Nunemacher, Jeffrey L.; Parker, Ellen M. Series: Spectrum S. Num Pages: 292 pages, 49 b/w illus. 307 exercises. BIC Classification: PBCD; PBV. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 228 x 152 x 17. Weight in Grams: 395. . 1999. 1st Edition. Paperback. . . . . . Bookseller Inventory # V9780521666466

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Book Description Paperback. Book Condition: New. Not Signed; 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. book. Bookseller Inventory # ria9780521666466_rkm

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Book Description Cambridge University Press. Book Condition: New. An introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. Series Editor(s): Watkins, William; Alexanderson, Gerald L.; Choudhury, Dipa; Firey, William J.; Kalman, Dan; Lang, Eleanor; Merris, Russell L.; Nunemacher, Jeffrey L.; Parker, Ellen M. Series: Spectrum S. Num Pages: 292 pages, 49 b/w illus. 307 exercises. BIC Classification: PBCD; PBV. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 228 x 152 x 17. Weight in Grams: 395. . 1999. 1st Edition. Paperback. . . . . Books ship from the US and Ireland. Bookseller Inventory # V9780521666466

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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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