کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594121 1630676 2014 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Critical numbers of natural intervals
ترجمه فارسی عنوان
تعداد بحرانی فواصل طبیعی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In this paper we study the critical numbers cr(r,n)cr(r,n) of natural intervals [r,n][r,n]. The critical number cr(1,n)cr(1,n) is the smallest integer l   satisfying the following conditions: (i) every sequence of integers S={r1=1⩽r2⩽⋯⩽rk}S={r1=1⩽r2⩽⋯⩽rk} with r1+⋯+rk=nr1+⋯+rk=n and k⩾lk⩾l has the following property: every integer between 1 and n can be written as a sum of distinct elements of S, and (ii) there exists S   with k=lk=l, satisfying this property. The definition of cr(r,n)cr(r,n) for r>1r>1 is a natural extension of cr(1,n)cr(1,n). We completely determined the values of cr(1,n)cr(1,n) and cr(2,n)cr(2,n). For r>2r>2, we determined the values of cr(r,n)cr(r,n) for n>3r2n>3r2. Similar problems concerning subsets of finite groups were introduced by Erdös and Heilbronn in 1964 and extended by other authors.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 138, May 2014, Pages 69–83
نویسندگان
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