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Existence of Steiner systems that admit automorphisms with large cycles

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
Related URLs:
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https://doi.org/10.1515/9783110198119.305DOIArticle
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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