Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory
Publication
, Journal Article
Calderbank, AR
Published in: European Journal of Combinatorics
January 1, 1988
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.
Duke Scholars
Published In
European Journal of Combinatorics
DOI
ISSN
0195-6698
Publication Date
January 1, 1988
Volume
9
Issue
2
Start / End Page
171 / 173
Related Subject Headings
- Computation Theory & Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Calderbank, A. R. (1988). Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory. European Journal of Combinatorics, 9(2), 171–173. https://doi.org/10.1016/S0195-6698(88)80043-X
Calderbank, A. R. “Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory.” European Journal of Combinatorics 9, no. 2 (January 1, 1988): 171–73. https://doi.org/10.1016/S0195-6698(88)80043-X.
Calderbank AR. Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory. European Journal of Combinatorics. 1988 Jan 1;9(2):171–3.
Calderbank, A. R. “Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory.” European Journal of Combinatorics, vol. 9, no. 2, Jan. 1988, pp. 171–73. Scopus, doi:10.1016/S0195-6698(88)80043-X.
Calderbank AR. Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory. European Journal of Combinatorics. 1988 Jan 1;9(2):171–173.
Published In
European Journal of Combinatorics
DOI
ISSN
0195-6698
Publication Date
January 1, 1988
Volume
9
Issue
2
Start / End Page
171 / 173
Related Subject Headings
- Computation Theory & Mathematics
- 0101 Pure Mathematics