Applegate, David and Rains, E. M. and Sloane, N. J. A. (2003) On asymmetric coverings and covering numbers. Journal of Combinatorial Designs, 11 (3). pp. 218-228. ISSN 1063-8539. doi:10.1002/jcd.10022. https://resolver.caltech.edu/CaltechAUTHORS:20171011-152858004
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Abstract
An asymmetric covering D(n,R) is a collection of special subsets S of an n-set such that every subset T of the n-set is contained in at least one special S with |S| - |T| ≤ R. In this paper we compute the smallest size of any D(n,1) for n ≤ 8. We also investigate “continuous” and “banded” versions of the problem. The latter involves the classical covering numbers C(n, k, k-1), and we determine the following new values: C(10, 5, 4) = 51, C(11, 7, 6) = 84, C(12, 8, 7) = 126, C(13, 9, 8) = 185 and C(14, 10, 9) = 259. We also find the number of non-isomorphic minimal covering designs in several cases.
| Item Type: | Article | ||||||||||||
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| Additional Information: | © 2003 Wiley Periodicals, Inc. Issue online: 18 April 2003; Version of record online: 18 April 2003; Manuscript Revised: 29 May 2002; Manuscript Received: 5 February 2002. | ||||||||||||
| Subject Keywords: | covering designs; covering numbers; Turán problem | ||||||||||||
| Issue or Number: | 3 | ||||||||||||
| DOI: | 10.1002/jcd.10022 | ||||||||||||
| Record Number: | CaltechAUTHORS:20171011-152858004 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171011-152858004 | ||||||||||||
| Official Citation: | Applegate, D., Rains, E. M. and Sloane, N. J. A. (2003), On asymmetric coverings and covering numbers. J. Combin. Designs, 11: 218–228. doi:10.1002/jcd.10022 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 82296 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 12 Oct 2017 16:21 | ||||||||||||
| Last Modified: | 15 Nov 2021 19:49 |
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