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On asymmetric coverings and covering numbers

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.

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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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URLURL TypeDescription Paper
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
Record Number:CaltechAUTHORS:20171011-152858004
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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
Deposited By: Tony Diaz
Deposited On:12 Oct 2017 16:21
Last Modified:15 Nov 2021 19:49

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