A note on the Tu-Deng conjecture

被引：3

作者：

Cheng Kaimin ^{[1
,2
]}

Hong Shaofang ^{[1
]}

Zhong Yuanming ^{[1
]}

机构：

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

[2] Sichuan Univ, Dept Math, Jinjiang Coll, Pengshan 620860, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2015年 / 28卷 / 03期

基金：

美国国家科学基金会;

关键词：

2-adic valuation; Tu-Deng conjecture; weight;

D O I：

10.1007/s11424-015-2240-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k be a positive integer. For any positive integer x = I pound (i=0) (a) x (i) 2 (i) , where x (i) = 0, 1, we define the weight w(x) of x by w(x) a parts per thousand" I pound (i=0) (a) x (i) . For any integer t with 0 < t < 2 (k) - 1, let S (t) a parts per thousand" {(a, b) a a"currency sign(2)|a + b a parts per thousand t (mod 2 (k) - 1), w(a) + w(b) < k, 0 a parts per thousand currency sign a, b a parts per thousand currency sign 2 (k) - 2}. This paper gives explicit formulas for cardinality of S (t) in the cases of w(t) a parts per thousand currency sign 3 and an upper bound for cardinality of S (t) when w(t) = 4. From this one then concludes that a conjecture proposed by Tu and Deng in 2011 is true if w(t) <= 4.

引用

页码：702 / 724

页数：23