کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897077 | 1630630 | 2018 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Asymptotically trivial linear homogeneous partition inequalities
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We consider linear homogeneous partition inequalities of the form(â)âk=1rakp(n+μk)â¤ââ=1sbâp(n+νâ), where p(n) is the number of integer partitions of n, {a1,a2,â¯,ar}, {b1,b2,â¯,bs} are positive integers, and 0â¤Î¼1<μ2<â¯<μr, 0â¤Î½1<ν2<â¯<νs are integers. From the fact that limnâââ¡p(n+μ)p(n)=1 (μ an integer) it follows that the inequality (â) can only hold if âk=1rakâ¤ââ=1sbâ. If the last relation is a strict inequality than (â) holds for all n>N, for an appropriately specified N, and can be established for all nâ¥1 by verifying that it holds for the finite set of cases specified by 1â¤nâ¤N. Such inequalities will be referred to as asymptotically trivial. Several examples of such inequalities are presented. The inequality (â) is trivial if the stronger condition âk=1rakp(μkâminâ¡(μ1,ν1)+1)â¤ââ=1sbâ holds, i.e., the supremum of the left-hand side of (â) is smaller than or equal to the infimum of its right-hand side. If âk=1rak=ââ=1sbâ then we say that (â) is non-trivial. In this case (â) can be an identity. A “conventional” proof, establishing the nature of (â) for all n, is required.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 184, March 2018, Pages 107-121
Journal: Journal of Number Theory - Volume 184, March 2018, Pages 107-121
نویسندگان
Jacob Katriel,