### 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 > k^{14}|a|=≤ N(N-1)(N-k) (k^{2}-k+1)(k^{2}-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 = (q^{t+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 |
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Pages (from-to) | 66-72 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 32 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1982 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**An intersection problem whose extremum is the finite projective space.** / Füredi, Z.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - An intersection problem whose extremum is the finite projective space

AU - Füredi, Z.

PY - 1982

Y1 - 1982

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=24244445123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24244445123&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(82)90065-6

DO - 10.1016/0097-3165(82)90065-6

M3 - Article

AN - SCOPUS:24244445123

VL - 32

SP - 66

EP - 72

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 1

ER -