Proofs and Confirmations pdf epub mobi txt 电子书下载 2024

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David M. Bressoud

Cambridge University Press

1999-08-13

292

USD 29.95

Paperback

9780521666466

图书标签: 组合数学数学 Math 经典

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发表于2024-11-27

Proofs and Confirmations epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

Proofs and Confirmations pdf epub mobi txt 电子书下载 2024

图书描述

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.

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Proofs and Confirmations pdf epub mobi txt 电子书下载

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q-级数的教材。显然，这不是一本q-级数的教材，原因是教我们的老师也不是专搞这个的，但最后反而因为这样，学到了更有意思的东西，大概是因为ASM确实是贯穿组合数学的一个重要课题，吸引了各个方向的专家，各种技巧都在这里展现。这部书较为完整地叙述了ASM猜想从诞生到解决的历程（最新的没有纳入），并且也着重强调，数学中的证明并不全为了说明事实准确而是为了更好地理解。

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平面分拆和交错矩阵理论位于组合数学，代数学，统计力学的交汇处，是一个非常美妙的理论。这本书是这一理论的最好入门读物，只要学过线性代数的基本知识即可。作者像讲故事一样娓娓叙来，给我们展开了一副美妙而又波澜壮阔的画卷。（我认为这本书是可以和 <<Proofs from the book>>并列的经典）

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