کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9515333 | 1343446 | 2005 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Crossing patterns of semi-algebraic sets
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Crossing patterns of semi-algebraic sets Crossing patterns of semi-algebraic sets](/preview/png/9515333.png)
چکیده انگلیسی
We prove that, for every family F of n semi-algebraic sets in Rd of constant description complexity, there exist a positive constant É that depends on the maximum complexity of the elements of F, and two subfamilies F1,F2âF with at least Én elements each, such that either every element of F1 intersects all elements of F2 or no element of F1 intersects any element of F2. This implies the existence of another constant δ such that F has a subset Fâ²âF with nδ elements, so that either every pair of elements of Fâ² intersect each other or the elements of Fâ² are pairwise disjoint. The same results hold when the intersection relation is replaced by any other semi-algebraic relation. We apply these results to settle several problems in discrete geometry and in Ramsey theory.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 2, August 2005, Pages 310-326
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 2, August 2005, Pages 310-326
نویسندگان
Noga Alon, János Pach, Rom Pinchasi, RadoÅ¡ RadoiÄiÄ, Micha Sharir,