کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11017677 | 1722376 | 2019 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Two extremal problems on intersecting families
ترجمه فارسی عنوان
دو مشکل افراطی در خانواده های تقسیم شده
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
In this short note, we address two problems in extremal set theory regarding intersecting families. The first problem is a question posed by Kupavskii: is it true that given two disjoint cross-intersecting families A,Bâ[n]k, they must satisfy min{|A|,|B|}â¤12nâ1kâ1? We give an affirmative answer for nâ¥2k2, and construct families showing that this range is essentially the best one could hope for, up to a constant factor. The second problem is a conjecture of Frankl. It states that for nâ¥3k, the maximum diversity of an intersecting family Fâ[n]k is equal to nâ3kâ2. We are able to find a construction beating the conjectured bound for n slightly larger than 3k, which also disproves a conjecture of Kupavskii.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 76, February 2019, Pages 1-9
Journal: European Journal of Combinatorics - Volume 76, February 2019, Pages 1-9
نویسندگان
Hao Huang,