# An intersection problem whose extremum is the finite projective space

Research output: Contribution to journalArticle

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### Abstract

Suppose that A is a finite set-system of N elements with the property |A ∩ A′| = 0, 1 or k for any two different A, A′ ε{lunate} A. We show that for N > k14|a|=≤ N(N-1)(N-k) (k2-k+1)(k2-2k+1)+ N(N-1) k(k-1)+N+1 where equality holds if and only if k = q + 1 (q is a prime power) N = (qt+1 - 1) (q - 1) and A is the set of subspaces of dimension at most two of the t-dimensional finite projective space of order q.

Original language English 66-72 7 Journal of Combinatorial Theory, Series A 32 1 https://doi.org/10.1016/0097-3165(82)90065-6 Published - 1982

Extremum Problem
Set Systems
Projective Space
Finite Set
Equality
Intersection
Subspace
If and only if

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

In: Journal of Combinatorial Theory, Series A, Vol. 32, No. 1, 1982, p. 66-72.

Research output: Contribution to journalArticle

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