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On Greatest Common Divisor of Subsequent Terms of Permutations(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2011年02期
Page:
18-22
Research Field:
数学
Publishing date:

Info

Title:
On Greatest Common Divisor of Subsequent Terms of Permutations
Author(s):
Ji Chengshuang
School of Mathematical Sciences,Nanjing Normal University,Nanjing,210046,China
Keywords:
permu tation of integers;  greatest comm on div isor;  lowe r lim it
PACS:
O156.1
DOI:
-
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.

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.

Memo

Memo:
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Last Update: 2011-06-15