کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593460 1630655 2016 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the minimum size of signed sumsets in elementary abelian groups
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the minimum size of signed sumsets in elementary abelian groups
چکیده انگلیسی

For a finite abelian group G and positive integers m and h, we letρ(G,m,h)=min⁡{|hA|:A⊆G,|A|=m} andρ±(G,m,h)=min⁡{|h±A|:A⊆G,|A|=m}, where hA   and h±Ah±A denote the h-fold sumset and the h-fold signed sumset of A  , respectively. The study of ρ(G,m,h)ρ(G,m,h) has a 200-year-old history and is now known for all G, m, and h  . In previous work we provided an upper bound for ρ±(G,m,h)ρ±(G,m,h) that we believe is exact, and proved that ρ±(G,m,h)ρ±(G,m,h) agrees with ρ(G,m,h)ρ(G,m,h) when G   is cyclic. Here we study ρ±(G,m,h)ρ±(G,m,h) for elementary abelian groups G; in particular, we determine all values of m   for which ρ±(Zp2,m,2) equals ρ(Zp2,m,2) for a given prime p.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 159, February 2016, Pages 384–401
نویسندگان
, ,