کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10118312 | 1632742 | 2019 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Families of sets with no matchings of sizes 3 and 4
ترجمه فارسی عنوان
خانواده های مجموعه ای بدون مابقی اندازه های 3 و 4
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
In this paper, we study the following classical question of extremal set theory: what is the maximum size of a family of subsets of [n] such that no s sets from the family are pairwise disjoint? This problem was first posed by ErdÅs and resolved for nâ¡0,â1(mods) by Kleitman in the 60s. Very little progress was made on the problem until recently. The only result was a very lengthy resolution of the case s=3,nâ¡1(mod3) by Quinn, which was written in his PhD thesis and never published in a refereed journal. In this paper, we give another, much shorter proof of Quinn's result, as well as resolve the case s=4,nâ¡2(mod4). This complements the results in our recent paper, where, in particular, we answered the question in the case nâ¡â2(mods) for sâ¥5.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 75, January 2019, Pages 123-135
Journal: European Journal of Combinatorics - Volume 75, January 2019, Pages 123-135
نویسندگان
Peter Frankl, Andrey Kupavskii,