科研之友
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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.
- 出版日期2015-6
- 单位四川大学
