[1]姬成双.排列中相邻两项的最大公因子[J].南京师大学报(自然科学版),2011,34(02):18-22.
　Ji Chengshuang.On Greatest Common Divisor of Subsequent Terms of Permutations[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(02):18-22.
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排列中相邻两项的最大公因子()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第34卷
期数:
2011年02期
页码:
18-22
栏目:
数学
出版日期:
2011-06-20

文章信息/Info

Title:
On Greatest Common Divisor of Subsequent Terms of Permutations
作者:
姬成双
南京师范大学数学科学学院, 江苏南京210046
Author(s):
Ji Chengshuang
School of Mathematical Sciences,Nanjing Normal University,Nanjing,210046,China
关键词:
整数排列;  最大公因子;  下极限
Keywords:
permu tation of integers;  greatest comm on div isor;  lowe r lim it
分类号:
O156.1
摘要:
1983年,Erds P,Freud R和Hegyvári N证明了对所有正整数的任一排列a1,a2,a3,…,有liminfi(ai,ai+1)/i≤61/90.本文将结果改进为liminfi(ai,ai+1)/i≤13/20.
Abstract:
In 1983, E rd??s P, Freud R and H egyv??ri N proved tha t lim in fi ( ai, ai+ 1 ) i ?? 61 90 for any in finite perm utation a1, a2, a3, ?? o f a ll positive integers. In th is pape r, a be tter upper bound lim infi ( ai, ai+ 1 ) i ?? 13 20 w as g iven.

参考文献/References:

[ 1] ?? Freud R. On sum s of subsequent term s o f perm utations[ J]. Ac taM ath Hunga r, 1983, 41( 1 /2): 177??185.
[ 2] ?? Dvornic ich R. On a prob lem of cyc lic pe rmuta tions of in tege rs[ J]. D iscrete App lM a th, 1980, 2( 4): 353??355.
[ 3] ?? S idorenko A F. An infin ite pe rmuta tion w ithout ar ithm e tic progress ions[ J]. DiscreteM a th, 1988, 69( 2): 211.
[ 4] ?? Po lyakovA B. On equ ilibrium d istr ibu tions on the set o f perm utations o f integ ers[ J]. RussianM ath Surveys, 1999, 54( 2):450??452.
[ 5] ?? Erd??s P, Freud R, H egyv??r i N. A rithm etical properties o f permuta tions o f integers[ J] . A ctaM ath Hunga r, 1983, 41 ( 1 /2): 169??176.
[ 6] ?? Sa ias E. Applications des entiers ?? d iv iseurs denses[ J]. Acta Ar ith, 1998, 83( 3): 225??240.

备注/Memo

备注/Memo:
通讯联系人: 姬成双, 硕士, 研究方向: 数论. E-m ail:jichengshuang@ 126. com
更新日期/Last Update: 2011-06-15