کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776769 | 1413640 | 2017 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The maximum product of sizes of cross-intersecting families
ترجمه فارسی عنوان
حداکثر محصول اندازه خانواده های متقابل
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
خانواده متقابل، خانواده های متقاطع
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
A set of sets is called a family. Two families A and B are said to be cross-
t-intersecting if each set in A intersects each set in B in at least t elements. For a family F, let l(F,t) denote the size of a largest subfamily of F whose sets have at least t common elements. We call F a (â¤r)-family if each set in F has at most r elements. We show that for any positive integers r, s and t, there exists an integer c(r,s,t) such that the following holds. If A is a subfamily of a (â¤r)-family F with l(F,t)â¥c(r,s,t)l(F,t+1), B is a subfamily of a (â¤s)-family G with l(G,t)â¥c(r,s,t)l(G,t+1), and A and B are cross-t-intersecting, then |A||B|â¤l(F,t)l(G,t). We give c(r,s,t) explicitly. Some known results follow from this, and we identify several natural classes of families for which the bound is attained.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 9, September 2017, Pages 2307-2317
Journal: Discrete Mathematics - Volume 340, Issue 9, September 2017, Pages 2307-2317
نویسندگان
Peter Borg,