1. Rich Words in the Block Reversal of a Word
- Author
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Mahalingam, Kalpana, Maity, Anuran, and Pandoh, Palak
- Subjects
Mathematics - Combinatorics ,68R15, 68R01, 68R05 - Abstract
The block reversal of a word $w$, denoted by $\mathtt{BR}(w)$, is a generalization of the concept of the reversal of a word, obtained by concatenating the blocks of the word in the reverse order. We characterize non-binary and binary words whose block reversal contains only rich words. We prove that for a binary word $w$, richness of all elements of $\mathtt{BR}(w)$ depends on $l(w)$, the length of the run sequence of $w$. We show that if all elements of $\mathtt{BR}(w)$ are rich, then $2\leq l(w)\leq 8$. We also provide the structure of such words.
- Published
- 2023