Published February 28, 2009
| Published
Journal Article
Open
On set systems with restricted intersections modulo p and p-ary t-designs
- Creators
- Wilson, Richard M.
Abstract
We consider bounds on the size of families ℱ of subsets of a v-set subject to restrictions modulo a prime p on the cardinalities of the pairwise intersections. We improve the known bound when ℱ is allowed to contain sets of different sizes, but only in a special case. We show that if the bound for uniform families ℱ holds with equality, then ℱ is the set of blocks of what we call a p-ary t-design for certain values of t. This motivates us to make a few observations about p-ary t-designs for their own sake.
Additional Information
© 2009 Elsevier B.V. Received 13 November 2007; accepted 12 September 2008. Available online 23 October 2008. The author's research was supported by NSA Grant H98230-04-1-0037.Attached Files
Published - Wilson2009p1015Discrete_Math.pdf
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Wilson2009p1015Discrete_Math.pdf
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Additional details
- Eprint ID
- 15838
- Resolver ID
- CaltechAUTHORS:20090914-121114974
- National Security Agency
- H98230-04-1-0
- Created
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2009-09-18Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field