Wilson, Richard M. (2000) Existence of Steiner systems that admit automorphisms with large cycles. In: Codes and Designs: Proceedings of a conference honoring Professor Dijen K. Ray-Chaudhuri on the occasion of his 65th birthday. Ohio State University Mathematical Research Institute Publications. No.10. De Gruyter , Berlin, pp. 305-312. ISBN 9783110198119. http://resolver.caltech.edu/CaltechAUTHORS:20180802-155215256
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Abstract
For every integer k ≥ 2, we construct infinite families of Steiner systems S(2, k, ν) that have (1) an automorphism that permutes the v points in a single-cycle of length ν, (2) an automorphism that fixes one point and permutes the remaining ν – 1 points in a single cycle, or (3) an automorphism that fixes one point and permutes the remaining points in two cycles, of lengths r = (ν - 1)/(k – 1) and ν – r – 1. The designs we construct with property (2) are also resolvable.
| Item Type: | Book Section | ||||||
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| Additional Information: | © 2000 by Walter de Gruyter GmbH. | ||||||
| Classification Code: | 2000 Mathematics Subject Classification: primary 05B05; secondary 05B25 | ||||||
| Record Number: | CaltechAUTHORS:20180802-155215256 | ||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20180802-155215256 | ||||||
| Official Citation: | Richard M. Wilson (2002). Existence of Steiner systems that admit automorphisms with large cycles. In Codes and Designs: Proceedings of a conference honoring Professor Dijen K. Ray-Chaudhuri on the occasion of his 65th birthday. The Ohio State University May 18-21, 2000 (pp. 305–312). https://doi.org/10.1515/9783110198119.305 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 88552 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 02 Aug 2018 23:05 | ||||||
| Last Modified: | 02 Aug 2018 23:05 |
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