On the number of tetrahedra with minimum, unit, and distinct volumes in three-space

@article{Dumitrescu2007OnTN,
  title={On the number of tetrahedra with minimum, unit, and distinct volumes in three-space},
  author={A. Dumitrescu and Csaba D. T{\'o}th},
  journal={Combinatorics, Probability and Computing},
  year={2007},
  volume={17},
  pages={203 - 224}
}
We formulate and give partial answers to several combinatorial problems on four-tuples of <i>n</i> points in three-space. (i) The number of minimum (nonzero) volume tetrahedra spanned by <i>n</i> points in R<sup>3</sup> is Θ(n<sup>3</sup>). (ii) The number of unit-volume tetrahedra determined by <i>n</i> points in R<sup>3</sup> is O(n<sup>7/2</sup>), and there are point sets for which this number is ω(n<sup>3</sup> log log n). (iii) The tetrahedra determined by <i>n</i> points in R<sup>3</sup… Expand
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