کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4656273 | 1343428 | 2008 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On additive and multiplicative Hilbert cubes
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
Given subset E of natural numbers FS(E) is defined as the collection of all sums of elements of finite subsets of E and any translation of FS(E) is said to be Hilbert cube. We can define the multiplicative analog of Hilbert cube as well. E.G. Strauss proved that for every ε>0 there exists a sequence with density >1−ε which does not contain an infinite Hilbert cube. On the other hand, Nathanson showed that any set of density 1 contains an infinite Hilbert cube. In the present note we estimate the density of Hilbert cubes which can be found avoiding sufficiently sparse (in particular, zero density) sequences. As a consequence we derive a result in which we ensure a dense additive Hilbert cube which avoids a multiplicative one.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 115, Issue 2, February 2008, Pages 354-360
Journal: Journal of Combinatorial Theory, Series A - Volume 115, Issue 2, February 2008, Pages 354-360