Proofs and confirmations: the story of the alternating sign matrix conjecture
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...
Gespeichert in:
| Beteilige Person: | |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
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| Schriftenreihe: | Spectrum
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| Links: | https://doi.org/10.1017/CBO9780511613449 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xv, 274 Seiten) |
| ISBN: | 9780511613449 |
Internformat
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| spelling | Bressoud, David M. 1950- Proofs and confirmations the story of the alternating sign matrix conjecture David M. Bressoud Proofs & Confirmations Cambridge Cambridge University Press 1999 1 Online-Ressource (xv, 274 Seiten) txt c cr 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. Erscheint auch als Druck-Ausgabe 9780521661706 Erscheint auch als Druck-Ausgabe 9780521666466 |
| spellingShingle | Bressoud, David M. 1950- Proofs and confirmations the story of the alternating sign matrix conjecture |
| title | Proofs and confirmations the story of the alternating sign matrix conjecture |
| title_alt | Proofs & Confirmations |
| title_auth | Proofs and confirmations the story of the alternating sign matrix conjecture |
| title_exact_search | Proofs and confirmations the story of the alternating sign matrix conjecture |
| title_full | Proofs and confirmations the story of the alternating sign matrix conjecture David M. Bressoud |
| title_fullStr | Proofs and confirmations the story of the alternating sign matrix conjecture David M. Bressoud |
| title_full_unstemmed | Proofs and confirmations the story of the alternating sign matrix conjecture David M. Bressoud |
| title_short | Proofs and confirmations |
| title_sort | proofs and confirmations the story of the alternating sign matrix conjecture |
| title_sub | the story of the alternating sign matrix conjecture |
| work_keys_str_mv | AT bressouddavidm proofsandconfirmationsthestoryofthealternatingsignmatrixconjecture AT bressouddavidm proofsconfirmations |