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On the number of unit-area triangles spanned by convex grids in the planeстатья
- Автор: Шкредов И.Д.
- Журнал: Computational Geometry: Theory and Applications
- Год издания: 2016
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Аннотация: A finite set of real numbers is called convex if the differences between consecutive elements form a strictly increasing sequence. We show that, for any pair of convex sets $A, B\subset\reals$, each of size $n^{1/2}$, the convex grid $A\times B$ spans at most $O(n^{37/17}\log^{2/17}n)$ unit-area triangles. Our analysis also applies to more general families of sets $A$, $B$, known as sets of Szemer\'edi--Trotter type.
- Добавил в систему: Шкредов Илья Дмитриевич