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arXiv · 1811.11739

Insertions Yielding Equivalent Double Occurrence Words

Daniel A. Cruz·Margherita Maria Ferrari·Natasa Jonoska·Lukas Nabergall·Masahico Saito
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Abstract

A double occurrence word (DOW) is a word in which every symbol appears exactly twice; two DOWs are equivalent if one is a symbol-to-symbol image of the other. We consider the so called repeat pattern ($\alpha\alpha$) and the return pattern ($\alpha\alpha^R$), with gaps allowed between the $\alpha$'s. These patterns generalize square and palindromic factors of DOWs, respectively. We introduce a notion of inserting repeat/return words into DOWs and study how two distinct insertions into the same word can produce equivalent DOWs. Given a DOW $w$, we characterize the structure of $w$ which allows two distinct insertions to yield equivalent DOWs. This characterization depends on the locations of the insertions and on the length of the inserted repeat/return words and implies that when one inserted word is a repeat word and the other is a return word, then both words must be trivial (i.e., have only one symbol). The characterization also introduces a method to generate families of words recursively.

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Daniel A. Cruz, Margherita Maria Ferrari, Natasa Jonoska, Lukas Nabergall, Masahico Saito. 2018-11-28. Insertions Yielding Equivalent Double Occurrence Words. https://arxiv.org/abs/1811.11739

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