Gaps and steps for the sequence nθ mod 1
Gaps and steps for the sequence nθ mod 1
复制标题
序列 nθ mod 1 的间隙和步长
DOI：
10.1017/s0305004100042195
复制
发表时间：
1967
影响因子：
0.8
通讯作者：
N. Slater
中科院分区：
文献类型：
--
作者：
N. Slater
对于给定的θ（0 < θ < 1）且r = 0，1，2，3，.，在分数部分{rθ}上有两个相关问题，即：差距问题：对于任意φ（0 < φ < 1）来确定连续r之间的间隙，对于该间隙，步骤问题：对于以升序重新排列的集合，以确定间隔[0，1]由此被划分成的步长。还有一些次要的问题，如不同长度的间隙或台阶的数目，以及当（2）按顺序排列时1，...，N的排列。
For a given θ(0 < θ < 1) and r = 0, 1, 2, 3,… there are two related problems on the fractional parts {rθ}, namely: the gap problem: for any φ (0 < φ < 1) to determine the gaps between the successive r for which the step problem: for the set rearranged in ascending order, to determine the steps into which the interval [0,1] is thereby partitioned. There are subsidiary problems of the numbers of gaps or steps of the various lengths, and also of the permutation of 1,…, N when (2) is arranged in order.