THE 2-ADIC VALUATIONS OF STIRLING NUMBERS OF THE SECOND KIND

被引：17

作者：

Hong, Shaofang ^{[1
]}

Zhao, Jianrong ^{[2
]}

机构：

[1] Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China

[2] SW Univ Finance & Econ, Sch Econ Math, Chengdu 610074, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2012年 / 8卷 / 04期

基金：

美国国家科学基金会;

关键词：

2-Adic valuation; Stirling number of the second kind; partition;

D O I：

10.1142/S1793042112500625

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the 2-adic valuations of the Stirling numbers S(n, k) of the second kind. We show that v(2)(S(4i, 5)) = v(2)(S(4i + 3, 5)) if and only if i not equivalent to 7 (mod 32). This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that v(2)(S(2(n) + 1, k + 1)) = s(2)(n) - 1 for any positive integer n, where s(2)(n) is the sum of binary digits of n. It proves another conjecture of Amdeberhan, Manna and Moll.

引用

页码：1057 / 1066

页数：10

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