Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory

Journal Article (Journal Article)

We apply duality in the Johnson scheme J(v, k) to give a very short proof of a theorem of Frankl and Füredi. We consider a family ℱ of k-subsets of a v-set such that ℱ is a 1-design and |x ∪ y| ⩾ λ > 0 for all x, y ∈ ℱ. We prove v ⩽ (k2 − k + λ)/λ with equality if and only if ℱ is a symmetric 2 − (v, k, λ) design. © 1988, Academic Press Limited. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Calderbank, AR

Published Date

  • January 1, 1988

Published In

Volume / Issue

  • 9 / 2

Start / End Page

  • 171 - 173

International Standard Serial Number (ISSN)

  • 0195-6698

Digital Object Identifier (DOI)

  • 10.1016/S0195-6698(88)80043-X

Citation Source

  • Scopus