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.

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College, Minnesota. He is Chair of the MAA Committee on the Undergraduate Program in Mathematics and Chair-Elect of the MAA Special Interest Group on Teaching Advanced High School Mathematics.

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**Book Description **CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1999. Paperback. Condition: New. 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. Seller Inventory # AAV9780521666466

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**Book Description **CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1999. Paperback. Condition: New. 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. Seller Inventory # AAV9780521666466

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