### 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 (US) |
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Pages (from-to) | 205-210 |

Number of pages | 6 |

Journal | European Journal of Combinatorics |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1985 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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## Cite this

Alon, N., Füredi, Z., & Katchalski, M. (1985). Separating Pairs of Points by Standard Boxes.

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