Proofs and Confirmations

The Story of the Alternating-Sign Matrix Conjecture
Erscheinungsjahr 2011
ISBN: 978-0-521-66646-6
Verlag: Cambridge University Press

Buch, Englisch, 290 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 478 g

Reihe: Spectrum

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.

Autoren/Hrsg.

Bressoud, David M.

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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