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Using the existence of t-designs to prove Erdős–Ko–Rado

par Godsil, Chris;Guo, Krystal
Référence Discrete mathematics, 342, 10, page (2846-2849)
Publication Publié, 2019-10

Article révisé par les pairs

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Résumé :

In 1984, Wilson proved the Erdős–Ko–Rado theorem for t-intersecting families of k-subsets of an n-set: he showed that if n≥(t+1)(k−t+1) and F is a family of k-subsets of an n-set such that any two members of F have at least t elements in common, then [Formula presented]. His proof made essential use of a matrix whose origin is not obvious. In this paper we show that this matrix can be derived, in a sense, as a projection of t-(n,k,1) design.