An intersection problem whose extremum is the finite projective space

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)66-72
Number of pages7
JournalJournal of Combinatorial Theory, Series A
Volume32
Issue number1
DOIs
Publication statusPublished - 1982

Fingerprint

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

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

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

Research output: Contribution to journalArticle

@article{f96ce9e0f790435382215904f2d484b6,
title = "An intersection problem whose extremum is the finite projective space",
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.",
author = "Z. F{\"u}redi",
year = "1982",
doi = "10.1016/0097-3165(82)90065-6",
language = "English",
volume = "32",
pages = "66--72",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
number = "1",

}

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 -