Palindromic permutations and generalized Smarandache palindromic permutations

Details Palindromic permutations and generalized Smarandache palindromic permutations Palindromic permutations and generalized Smarandache palindromic permutations

2006-07-28

arxiv.org/abs/math/0607742v2

Scientia Magna Journal, Vol. 2, No. 3 (2006), pp. 65-77

Mathematics

General Mathematics

14 pages

Scientific paper

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.

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