Unit Distances in Three Dimensions
نویسندگان
چکیده
We show that the number of unit distances determined by n points in R is O(n), slightly improving the bound of Clarkson et al. [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [25].
منابع مشابه
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 21 شماره
صفحات -
تاریخ انتشار 2012