HIERARCHIES OF PALINDROMIC SEQUENCES IN THE SYMMETRIC GROUP Sn
Journal Title: Journal of Ramanujan Society of Mathematics and Mathematical Sciences - Year 2017, Vol 6, Issue 1
Abstract
A new property of the Symmetric group, Sn, arises when each element is assigned a unique place value, which enables the ordering of the elements (nu- merically). It is shown that the di erences between successive elements of this ordered, place-value assigned symmetric group Sn, give rise to a palindromic se- quence (Pk) 1kn!1. We de ne the family of palindromic sequences, associated to Sn. Sieving out a given number at a time in the maximal palindromic sequence of the group, Sn, of length n! 1, results in a hierarchy of palindromic sequences, ending with a single element, which will be the central element of (Pk) 1kn!1. Consequences of the concept of place value ordering of the elements of Sn, are presented in this article.
Authors and Affiliations
K. Srinivasa Rao, Pankaj Pundir
Keywords
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