کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903169 | 1632403 | 2018 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Distinct distances between a collinear set and an arbitrary set of points
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Distinct distances between a collinear set and an arbitrary set of points Distinct distances between a collinear set and an arbitrary set of points](/preview/png/8903169.png)
چکیده انگلیسی
We consider the number of distinct distances between two finite sets of points in Rk, for any constant dimension kâ¥2, where one set P1 consists of n points on a line l, and the other set P2 consists of m arbitrary points, such that no hyperplane orthogonal to l and no hypercylinder having l as its axis contains more than O(1) points of P2. The number of distinct distances between P1 and P2 is then Ωminn2â3m2â3,n10â11m4â11log2â11m,n2,m2.Without the assumption on P2, there exist sets P1, P2 as above, with only O(m+n) distinct distances between them.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 341, Issue 1, January 2018, Pages 261-265
Journal: Discrete Mathematics - Volume 341, Issue 1, January 2018, Pages 261-265
نویسندگان
Ariel Bruner, Micha Sharir,