Block reversal on finite words

Abstract

The block reversal of a word is a generalization of the concept of reversal of a word where in place of reversing individual letters, we take the blocks of the word in the reverse order. Since there can be multiple ways in which a word can be divided into blocks, the block reversal of a word forms a set. We study some properties of the block reversal of a word. We characterize words that have the same block reversal set. We find a relation between the block reversal and the non-overlapping inversion defined by Schöniger and Waterman in the year 1992. We characterize words with the minimum and the maximum number of elements in the block reversal. We then study the distribution of palindromes in the block reversal of a word.