A permutation over alphabet Σ=(1,2,3,…,n)Σ=(1,2,3,…,n) is a sequence over ΣΣ, where every element occurs exactly once. SnSn denotes symmetric group defined over ΣΣ. In=(1,2,3,…,n)∈SnIn=(1,2,3,…,n)∈Sn denotes the Identity permutation. Rn∈SnRn∈Sn is the reverse permutation i.e., Rn=(n,n−1,n−2,…,2,1)Rn=(n,n−1,n−2,…,2,1). An operation, that we call as an LE operation, has been defined which consists of exactly two generators: set-rotate that we call Rotate and pair-exchange that we call Exchange (OEIS). At least two generators are the required to generate SnSn. Rotate rotates all elements to the left (moves leftmost element to the right end) and Exchange is the pair-wise exchange of the two leftmost elements. The optimum number of moves for transforming RnRn into InIn with LE operation are known for n≤10n≤10; as listed in OEIS with identity A048200. However, no general upper bound is known. The contributions of this article are: (a) a novel upper bound for the number of moves required to sort RnRn with LE has been derived; (b) the optimum number of moves to sort the next larger RnRn i.e., R11R11 has been computed; (c) an algorithm conjectured to compute the optimum number of moves to sort a given RnRn has been designed.
