Proofs and Confirmations 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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David M. Bressoud 作者

Cambridge University Press

译者

1999-8-13 出版日期

290 页数

USD 103.99 价格

Hardcover

Spectrum Series 丛书系列

9780521661706 图书编码

Proofs and Confirmations 在线电子书图书标签: 数学其余代数7

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Proofs and Confirmations 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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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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