ENGLISH

Proofs and confirmations: the story of the alternating sign matrix conjecture

By David M. Bressoud

Book information

Publisher
Cambridge University Press
Year
1999
ISBN
0521666465, 9780521666466
LCC
QA188 .B73 1999
Open Library ID
OL35427M
Language
english
Format
DJVU
Filesize
3 MB (2804279 bytes)
Series
Spectrum
Edition
CUP
Pages
292\292
Library
Kolxo3
DPI
300
Orientation
yes
Scanned
no
Time added
2009-07-20 03:45:11

Description

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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