کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4655337 | 1632946 | 2014 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Forbidding just one intersection, for permutations
ترجمه فارسی عنوان
ممنوع دادن فقط یک تقاطع، برای جایگزینی
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کلمات کلیدی
تغییرات تقاطع ها، ثبات،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
We prove that for n sufficiently large, if A is a family of permutations of {1,2,â¦,n} with no two permutations in A agreeing exactly once, then |A|â¤(nâ2)!, with equality holding only if A is a coset of the stabilizer of 2 points. We also obtain a Hilton-Milner type result, namely that if A is such a family which is not contained within a coset of the stabilizer of 2 points, then it is no larger than the familyB={ÏâSn:Ï(1)=1,Ï(2)=2,B=#{fixed points of Ïâ¥5}â 1}B=âª{(13)(24),(14)(23),(1324),(1423)} We conjecture that for tâN, and for n sufficiently large depending on t, if A is family of permutations of {1,2,â¦,n} with no two permutations in A agreeing exactly tâ1 times, then |A|â¤(nât)!, with equality holding only if A is a coset of the stabilizer of t points. This can be seen as a permutation analogue of a conjecture of ErdÅs on families of k-element sets with a forbidden intersection, proved by Frankl and Füredi in [9].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 126, August 2014, Pages 136-165
Journal: Journal of Combinatorial Theory, Series A - Volume 126, August 2014, Pages 136-165
نویسندگان
David Ellis,