## Abstract

Let l_{1} denote the metric space the elements of which are all sequences x=(x_{1}, x_{2},...) of real numbers satisfying ∑ i=1∞ |xi|<∞. The distance d(x, y) between x and y = (y_{1}, y_{2},...) is d(x,y)=∑ i=1∞ |xi−yi|. Let υ_{0}, υ_{1},..., υ_{m−1}, u_{0}, u_{1},...,u_{k-1} be a sequence of n = m + k not necessarily distinct vectors in l_{1}, where k > 0, m = k + 2u + 1 and u ⩾ 0. We show that ∑ 0⩽i<j<m (i−j)(modm)∈{±1,±2...,±u} d(υi,υj)+∑ 0⩽i<m 0⩽j<k d(υi,uj)⩾∑ 0⩽i<j<m d(υi,υj)+∑ 0⩽i<j<k d(ui,uj). This solves a conjecture of Deza and Laurent and implies, as special cases, inequalities of Deza, Laurent, Kelly, Barahona and Mahjoub.

Original language | English (US) |
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Pages (from-to) | 1-5 |

Number of pages | 5 |

Journal | European Journal of Combinatorics |

Volume | 11 |

Issue number | 1 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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