DMCA
Palindromic Permutations and Generalized Smarandache Palindromic Permutations ∗† (2006)
BibTeX
@MISC{Lá06palindromicpermutations,
author = {Tèmítópé Gbóláhàn Jaíyéo. Lá},
title = {Palindromic Permutations and Generalized Smarandache Palindromic Permutations ∗†},
year = {2006}
}
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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 Sn of degree n. It is shown that in Sn, there exist a LPP and a RPP and they are unique(this fact is demonstrated using S2 and S3). The dihedral group Dn is shown to be generated by a RGSPP and a LGSPP(this is observed to be true in S3) but the geometric interpretations of a RGSPP and a LGSPP are found not to be rotation and reflection respectively. In S3, each permutation is at least a RGSPP or a LGSPP. There are 4 RGSPPs and 4 LGSPPs in S3, while 2 permutations are both RGSPPs and LGSPPs. A permutation in Sn 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. 1
