Join Our Newsletter

Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Pinyin
i2Cantonese
i2Cangjie
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

CCCG

2008

2008

A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vectors, it is called parallelogram free. We show that there exist n-element point sets in the plane in general position, and parallelogram free, that determine only O(n2 / log n) distinct distances. This answers a question of Erdos, Hickerson and Pach. We then revisit an old problem of Erdos : given any n points in the plane (or in d dimensions), how many of them can one select so that the distances which are determined are all distinct? -- and provide (make explicit) some new bounds in one and two dimensions. Other related distance problems are also discussed.

Related Content

Added |
29 Oct 2010 |

Updated |
29 Oct 2010 |

Type |
Conference |

Year |
2008 |

Where |
CCCG |

Authors |
Adrian Dumitrescu |

Comments (0)