کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4655268 | 1632944 | 2014 | 43 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An Erdős–Ko–Rado theorem for cross t-intersecting families
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: An Erdős–Ko–Rado theorem for cross t-intersecting families An Erdős–Ko–Rado theorem for cross t-intersecting families](/preview/png/4655268.png)
چکیده انگلیسی
Two families AA and BB, of k-subsets of an n-set, are cross t-intersecting if for every choice of subsets A∈AA∈A and B∈BB∈B we have |A∩B|≥t|A∩B|≥t. We address the following conjectured cross t -intersecting version of the Erdős–Ko–Rado theorem: For all n≥(t+1)(k−t+1)n≥(t+1)(k−t+1) the maximum value of |A||B||A||B| for two cross t -intersecting families A,B⊂([n]k) is (n−tk−t)2. We verify this for all t≥14t≥14 except finitely many n and k for each fixed t. Further, we prove uniqueness and stability results in these cases, showing, for instance, that the families reaching this bound are unique up to isomorphism. We also consider a p-weight version of the problem, which comes from the product measure on the power set of an n-set.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 128, November 2014, Pages 207–249
Journal: Journal of Combinatorial Theory, Series A - Volume 128, November 2014, Pages 207–249
نویسندگان
Peter Frankl, Sang June Lee, Mark Siggers, Norihide Tokushige,