کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9513256 | 1632460 | 2005 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Kemnitz' conjecture revisited
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A conjecture of Kemnitz remained open for some 20 years: each sequence of 4n-3 lattice points in the plane has a subsequence of length n whose centroid is a lattice point. It was solved independently by Reiher and di Fiore in the autumn of 2003. A refined and more general version of Kemnitz' conjecture is proved in this note. The main result is about sequences of lengths between 3p-2 and 4p-3 in the additive group of integer pairs modulo p, for the essential case of an odd prime p. We derive structural information related to their zero sums, implying a variant of the original conjecture for each of the lengths mentioned. The approach is combinatorial.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 297, Issues 1â3, 28 July 2005, Pages 196-201
Journal: Discrete Mathematics - Volume 297, Issues 1â3, 28 July 2005, Pages 196-201
نویسندگان
Svetoslav Savchev, Fang Chen,