Computational and Constructive Design Theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
1996
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs |
| Physical Description: | 1 Online-Ressource (XIV, 362 p) |
| ISBN: | 9781475724974 9781475724998 |
| DOI: | 10.1007/978-1-4757-2497-4 |
Staff View
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| 500 | |a Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs | ||
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Record in the Search Index
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| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2497-4 |
| format | Electronic eBook |
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| isbn | 9781475724974 9781475724998 |
| language | English |
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| spelling | Wallis, W. D. Verfasser aut Computational and Constructive Design Theory edited by W. D. Wallis Boston, MA Springer US 1996 1 Online-Ressource (XIV, 362 p) txt rdacontent c rdamedia cr rdacarrier Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs Mathematics Computational complexity Algorithms Combinatorics Discrete Mathematics in Computer Science Mathematik Kombinatorische Designtheorie (DE-588)4164747-6 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Kombinatorische Designtheorie (DE-588)4164747-6 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-2497-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wallis, W. D. Computational and Constructive Design Theory Mathematics Computational complexity Algorithms Combinatorics Discrete Mathematics in Computer Science Mathematik Kombinatorische Designtheorie (DE-588)4164747-6 gnd |
| subject_GND | (DE-588)4164747-6 (DE-588)4143413-4 |
| title | Computational and Constructive Design Theory |
| title_auth | Computational and Constructive Design Theory |
| title_exact_search | Computational and Constructive Design Theory |
| title_full | Computational and Constructive Design Theory edited by W. D. Wallis |
| title_fullStr | Computational and Constructive Design Theory edited by W. D. Wallis |
| title_full_unstemmed | Computational and Constructive Design Theory edited by W. D. Wallis |
| title_short | Computational and Constructive Design Theory |
| title_sort | computational and constructive design theory |
| topic | Mathematics Computational complexity Algorithms Combinatorics Discrete Mathematics in Computer Science Mathematik Kombinatorische Designtheorie (DE-588)4164747-6 gnd |
| topic_facet | Mathematics Computational complexity Algorithms Combinatorics Discrete Mathematics in Computer Science Mathematik Kombinatorische Designtheorie Aufsatzsammlung |
| url | https://doi.org/10.1007/978-1-4757-2497-4 |
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