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| Paper Abstract and Keywords | ||
| Presentation | 2010-04-22 13:15 Complete classification of small realizable oriented matroids Hiroyuki Miyata, Sonoko Moriyama (Tokyo Univ.), Komei Fukuda (ETH Zurich)  COMP2010-4 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Enumerating combinatorial types of point configurations, hyperplane arrangements and convex polytopes are fundamental problems in combinatorial geometry and has been studied for a long time. However, most of them are for non-degenerate cases or 2-dimensional cases. Recently, Finschi and Fukuda developed a database of oriented matroids including non-uniform ones and ones of higher rank. Then many studies on the realizability problem, the problem to decide whether a given oriented matroid has the corresponding point configuration, have been done. However, they have not succeeded to classify the oriented matroids completely. In this paper, we decide the realizability of them completely. We give a complete classification of the realizability of rank-4 oriented matroids on 8 elements, rank-3 oriented matroids on 9 elements and rank-6 oriented matroids on 9 elements. As a result, we decide all possible combinatorial types of 8-element point configurations in 3-dimensional space, those of 9-element point configurations in 2-dimensional space and those in 5-dimensional space. We also determine all possible combinatorial types of 5-dimensional polytopes with 9 vertices using the result. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | oriented matroids / the realizability problem / point configurations / hyperplane arrangements / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 110, no. 12, COMP2010-4, pp. 25-31, April 2010. | |
| Paper # | COMP2010-4 | |
| Date of Issue | 2010-04-15 (COMP) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | COMP2010-4 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2010-04-22 - 2010-04-22 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Ritusmeikan University, Biwako-Kusatsu Campus |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2010-04-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Complete classification of small realizable oriented matroids |
| Sub Title (in English) | |
| Keyword(1) | oriented matroids |
| Keyword(2) | the realizability problem |
| Keyword(3) | point configurations |
| Keyword(4) | hyperplane arrangements |
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| 1st Author's Name | Hiroyuki Miyata |
| 1st Author's Affiliation | The University of Tokyo (Tokyo Univ.) |
| 2nd Author's Name | Sonoko Moriyama |
| 2nd Author's Affiliation | The University of Tokyo (Tokyo Univ.) |
| 3rd Author's Name | Komei Fukuda |
| 3rd Author's Affiliation | Swiss Federal Institute of Technology Zurich (ETH Zurich) |
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| Speaker | Author-1 |
| Date Time | 2010-04-22 13:15:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2010-4 |
| Volume (vol) | vol.110 |
| Number (no) | no.12 |
| Page | pp.25-31 |
| #Pages | 7 |
| Date of Issue | 2010-04-15 (COMP) |
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