Arithmetic properties of summands of partitions II

被引：6
|
作者：
Dartyge, C
Sárközy, A
机构：
[1] Univ Nancy 1, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France
[2] Eotvos Lorand Univ, Dept Algebra & Number Theory, H-1518 Budapest, Hungary
来源：
RAMANUJAN JOURNAL | 2005年 / 10卷 / 03期
关键词：
partitions; residue classes;
D O I：
10.1007/s11139-005-4855-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let d is an element of N, d >= 2. We prove that a positive proportion of partitions of an integer n satisfies the following : for all 1 <= a < b <= d, the number of the parts congruent to a (mod d) is greater than the number of the parts congruent to b (mod d). We also show that for almost all partitions the rate of the number of square free parts is 6/pi(2) (1 + o(1)).
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页码：383 / 394
页数：12
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