The 2-adic valuations of differences of Stirling numbers of the second kind

被引：5
|
作者：
Zhao, Wei [1 ,2 ]
Zhao, Jianrong [3 ]
Hong, Shaofang [1 ]
机构：
[1] Sichuan Univ, Math Coll, Chengdu 610064, Peoples R China
[2] Sci & Technol Commun Secur Lab, Chengdu 610041, Peoples R China
[3] Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 610074, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2015年 / 153卷
基金：
美国国家科学基金会;
关键词：
Stirling numbers of the second kind; 2-adic valuation; Ring of p-adic integers; Generating function; Convolution identity; DIVISIBILITY; CONGRUENCES;
D O I：
10.1016/j.jnt.2015.01.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let m, n, k and c be positive integers, v(2)(k) be the 2-adic valuation of k and S(n, k) be the Stirling numbers of the second kind. We show that if 2 <= m <= n and c is odd, then nu(2)(S(c2(n+1), 2(m) - 1) S(c2(n), 2(m) - 1)) = n + 1 except when n = m = 2 and c = 1, in which case nu(2)(S(8, 3) - S(4,3)) = 6. This solves a conjecture of Lengyel proposed in 2009. (C) 2015 Elsevier Inc. All rights reserved.
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页码：309 / 320
页数：12
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