کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4655556 | 1343390 | 2013 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Subsets of products of finite sets of positive upper density
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Subsets of products of finite sets of positive upper density Subsets of products of finite sets of positive upper density](/preview/png/4655556.png)
چکیده انگلیسی
In this note we prove that for every sequence (mq)q(mq)q of positive integers and for every real 0<δ≤10<δ≤1 there is a sequence (nq)q(nq)q of positive integers such that for every sequence (Hq)q(Hq)q of finite sets such that |Hq|=nq|Hq|=nq for every q∈Nq∈N and for every D⊆⋃k∏q=0k−1Hq with the property thatlimsupk|D∩∏q=0k−1Hq||∏q=0k−1Hq|≥δ there is a sequence (Jq)q(Jq)q, where Jq⊆HqJq⊆Hq and |Jq|=mq|Jq|=mq for all q , such that ∏q=0k−1Jq⊆D for infinitely many k . This gives us a density version of a well-known Ramsey-theoretic result. We also give some estimates on the sequence (nq)q(nq)q in terms of the sequence of (mq)q(mq)q.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 120, Issue 1, January 2013, Pages 183–193
Journal: Journal of Combinatorial Theory, Series A - Volume 120, Issue 1, January 2013, Pages 183–193
نویسندگان
Stevo Todorcevic, Konstantinos Tyros,