Palindromic Permutations and Generalized Smarandache Palindromic Permutations

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.