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Palindromic Permutations And Generalized Smarandache Palindromic Permutations

Name: Palindromic Permutations And Generalized Smarandache Palindromic Permutations
Creator: Temitope Gbolahan Jaiyeola
Keywords: General Mathematics (math.GM), FOS: Mathematics, symmetric groups, palindromic permutations, Mathematics - General Mathematics, 20B30

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2006Embargo end date: 01 Jan 2006Publisher:ZenodoJournal:viXra

Authors: Temitope Gbolahan Jaiyeola;

doi: 10.5281/zenodo.9128 , 10.5281/zenodo.9428 , 10.5281/zenodo.32322 , 10.48550/arxiv.math/0607742

arXiv: http://arxiv.org/abs/math/0607742

Palindromic Permutations And Generalized Smarandache Palindromic Permutations

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Abstract

The idea of left(right) palindromic permutations(LPPs,RPPs) and left(right) generalized Smarandache palindromic permutations(LGSPPs,RGSPPs) are introduced in symmetric groups S_n of degree n. It is shown that in S_n, there exist a LPP and a RPP and they are unique(this fact is demonstrated using S_2 and S_3). The dihedral group D_n is shown to be generated by a RGSPP and a LGSPP(this is observed to be true in S_3) but the geometric interpretations of a RGSPP and a LGSPP are found not to be rotation and reflection respectively. In S_3, each permutation is at least a RGSPP or a LGSPP. There are 4 RGSPPs and 4 LGSPPs in S_3, while 2 permutations are both RGSPPs and LGSPPs. A permutation in S_n is shown to be a LPP or RPP(LGSPP or RGSPP) if and only if its inverse is a LPP or RPP(LGSPP or RGSPP) respectively. Problems for future studies are raised.

14 pages

Related Organizations

OBAFEMI AWOLOWO UNIVERSITY
Nigeria
Obafemi Awolowo University
Nigeria

Keywords

General Mathematics (math.GM), FOS: Mathematics, symmetric groups, palindromic permutations, Mathematics - General Mathematics, 20B30

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