Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published April 18, 2003 | Submitted
Journal Article Open

On asymmetric coverings and covering numbers

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.

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.

Attached Files

Submitted - 0205303.pdf

Files

0205303.pdf
Files (136.1 kB)
Name Size Download all
md5:daf0d5820e9998c9a018c8c7cf4c9d92
136.1 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
March 5, 2024