کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4656403 | 1343435 | 2008 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Erdős–Ko–Rado theorems for permutations and set partitions
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let Sym([n]) denote the collection of all permutations of [n]={1,…,n}. Suppose A⊆Sym([n]) is a family of permutations such that any two of its elements (when written in its cycle decomposition) have at least t cycles in common. We prove that for sufficiently large n, |A|⩽(n−t)! with equality if and only if A is the stabilizer of t fixed points. Similarly, let B(n) denote the collection of all set partitions of [n] and suppose A⊆B(n) is a family of set partitions such that any two of its elements have at least t blocks in common. It is proved that, for sufficiently large n, |A|⩽Bn−t with equality if and only if A consists of all set partitions with t fixed singletons, where Bn is the nth Bell number.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 115, Issue 6, August 2008, Pages 1008-1020
Journal: Journal of Combinatorial Theory, Series A - Volume 115, Issue 6, August 2008, Pages 1008-1020