Proofs and Confirmations - David M. Bressoud

Proofs and Confirmations

The Story of the Alternating-Sign Matrix Conjecture
Buch | Softcover
292 Seiten
1999
Cambridge University Press (Verlag)
978-0-521-66646-6 (ISBN)
47,35 inkl. MwSt
An introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses.
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.

1. The conjecture; 2. Fundamental structures; 3. Lattice paths and plane partitions; 4. Symmetric functions; 5. Hypergeometric series; 6. Explorations; 7. Square ice.

Erscheint lt. Verlag 13.8.1999
Reihe/Serie Spectrum
Zusatzinfo Worked examples or Exercises; 12 Halftones, unspecified; 37 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 152 x 229 mm
Gewicht 430 g
Themenwelt Mathematik / Informatik Mathematik Graphentheorie
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 0-521-66646-5 / 0521666465
ISBN-13 978-0-521-66646-6 / 9780521666466
Zustand Neuware
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