Książka Proofs and Confirmations David M. Bressoud

Proofs and Confirmations

The Story of the Alternating-Sign Matrix Conjecture

Język: Angielski
Oprawa: Miękka
Dostępność: Dostępna u dostawcy
Wysyłamy za 14-21 dni
237.06
This is an introduction to recent developments in algebraic combinatorics and an illustration of how...

Informacje o książce

Język
Angielski
Oprawa
Książka - Miękka
Data wydania
1999
strony
292
EAN
9780521666466
ISBN
0521666465
Enbook ID
02039849
Waga
390
Wymiary
229 x 154 x 23

Pełny opis

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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