Arithmetical properties of permutations of integers
Arithmetical properties of permutations of integers
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DOI：
10.1007/bf01994075
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发表时间：
1983-03
影响因子：
0.9
通讯作者：
P. Erdos;P. Erdos;R. Freud;R. Freud;N. Hegyvári;N. Hegyvári
中科院分区：
文献类型：
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作者：
P. Erdos;P. Erdos;R. Freud;R. Freud;N. Hegyvári;N. Hegyvári
对于有限的情况下，让aa，作为..... a，是整数1、2、.的排列，n，并且对于无限情况，令a1，a2…az，.是所有正整数的排列。关于这类置换和相关问题的一些问题和结果可以在[2]中找到（特别参见第94页）。文[3]从几个角度估计了和ai+ ai+~的稠密性，本文将研究两个后继元素的最小公倍数和最大公约数。首先，我们处理最小公倍数。对于全同置换，我们有[al，a~+ d= i（i+ 1）.我们表明，适当的其他排列，这个值变得相当小。首先我们考虑有限情形
For the finite case let aa, as..... a, be a permutation of the integers 1, 2,..., n and for the infinite case let al, a2..... az,... be a permutation of all positive integers. Some problems and results concerning such permutations and related questions can be found in [2](see in particular p. 94). In [3] the density of the sums ai+ ai+~ is estimated from several points of view.In the present paper we shall investigate the least common multiple and the greatest common divisor of two subsequent elements. First we deal with the least common multiple. For the identical permutation we have [al, a~+ d= i (i+ 1). We show that for suitable other permutations this value becomes considerably smaller. First we consider the finite case