Geodesic
Constructions of words rich in palindromes and pseudopalindromes
Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3.

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A narrow connection between infinite binary words rich in classical palindromes and infinite binary words rich simultaneously in palindromes and pseudopalindromes (the so-called $H$-rich words) is demonstrated. The correspondence between rich and $H$-rich words is based on the operation $S$ acting over words over the alphabet $\{0,1\}$ and defined by $S(u_0u_1u_2\ldots) = v_1v_2v_3\ldots$, where $v_i= u_{i-1} + u_i \mod 2$. The operation $S$ enables us to construct a new class of rich words and a new class of $H$-rich words. Finally, the operation $S$ is considered on the multiliteral alphabet $\mathbb{Z}_m$ as well and applied to the generalized Thue--Morse words. As a byproduct, new binary rich and $H$-rich words are obtained by application of $S$ on the generalized Thue--Morse words over the alphabet $\mathbb{Z}_4$. 
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     author = {Pelantov\'a, Edita and Starosta, \v{S}t\v{e}p\'an},
     title = {Constructions of words rich in palindromes and pseudopalindromes},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2015-2016},
     doi = {10.46298/dmtcs.655},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.655/}
}
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Pelantová, Edita; Starosta, Štěpán. Constructions of words rich in palindromes and pseudopalindromes. Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3. doi : 10.46298/dmtcs.655. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.655/

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