### Abstract

Let A be a set of distinct points in ℝ^{d}. A 2-subset {a, b} of A is called separated if there exists a closed box with sides parallel to the axes, containing a and b but no other points of A. Let s(A) denote the number of separated 2-sets of A and put f(n, d) = max {s(A): A ⊂ ℝ^{d}, |A| = n}. We show that f(n, 2) = [n^{2}/4] + n − 2 for all n≥2 and that for each fixed dimension d f(n,d)=(1−1/2 2 d−1−1)⋅n2/2+o(n2).

Original language | English |
---|---|

Pages (from-to) | 205-210 |

Number of pages | 6 |

Journal | European Journal of Combinatorics |

Volume | 6 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1985 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*European Journal of Combinatorics*,

*6*(3), 205-210. https://doi.org/10.1016/S0195-6698(85)80028-7

**Separating Pairs of Points by Standard Boxes.** / Alon, Noga; Füredi, Z.; Katchalski, M.

Research output: Contribution to journal › Article

*European Journal of Combinatorics*, vol. 6, no. 3, pp. 205-210. https://doi.org/10.1016/S0195-6698(85)80028-7

}

TY - JOUR

T1 - Separating Pairs of Points by Standard Boxes

AU - Alon, Noga

AU - Füredi, Z.

AU - Katchalski, M.

PY - 1985/1/1

Y1 - 1985/1/1

N2 - Let A be a set of distinct points in ℝd. A 2-subset {a, b} of A is called separated if there exists a closed box with sides parallel to the axes, containing a and b but no other points of A. Let s(A) denote the number of separated 2-sets of A and put f(n, d) = max {s(A): A ⊂ ℝd, |A| = n}. We show that f(n, 2) = [n2/4] + n − 2 for all n≥2 and that for each fixed dimension d f(n,d)=(1−1/2 2 d−1−1)⋅n2/2+o(n2).

AB - Let A be a set of distinct points in ℝd. A 2-subset {a, b} of A is called separated if there exists a closed box with sides parallel to the axes, containing a and b but no other points of A. Let s(A) denote the number of separated 2-sets of A and put f(n, d) = max {s(A): A ⊂ ℝd, |A| = n}. We show that f(n, 2) = [n2/4] + n − 2 for all n≥2 and that for each fixed dimension d f(n,d)=(1−1/2 2 d−1−1)⋅n2/2+o(n2).

UR - http://www.scopus.com/inward/record.url?scp=85014877613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014877613&partnerID=8YFLogxK

U2 - 10.1016/S0195-6698(85)80028-7

DO - 10.1016/S0195-6698(85)80028-7

M3 - Article

VL - 6

SP - 205

EP - 210

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

IS - 3

ER -