Publications [#331062] of Robert Calderbank

Journal articles or Book chapters PUBLISHED

1. Calderbank, AR, Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory, European Journal of Combinatorics, vol. 9 no. 2 (January, 1988), pp. 171-173, Elsevier BV [doi]
   (last updated on 2026/01/17)

   Abstract:
   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.