On morphisms preserving palindromic richness
Francesco Dolce, Edita Pelantov\'a

TL;DR
This paper investigates specific morphisms in Class P_{ret} that generate new rich words from known ones, characterizing their properties and showing their preservation of palindromic richness over binary and larger alphabets.
Contribution
It characterizes P_{ret} morphisms that preserve palindromic richness and demonstrates their relation to Arnoux-Rauzy morphisms on larger alphabets.
Findings
P_{ret} morphisms preserving richness are characterized over binary alphabets.
Every Arnoux-Rauzy morphism is conjugated to a P_{ret} morphism and preserves richness.
The study extends the understanding of morphisms that generate rich words in combinatorics on words.
Abstract
It is known that each word of length contains at most distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite words. Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while episturmian words and words coding symmetric -interval exchange transformations give us other examples on larger alphabets. In this paper we look for morphisms of the free monoid, which allow us to construct new rich words from already known rich words. We focus on morphisms in Class . This class contains morphisms injective on the alphabet and satisfying a particular palindromicity property: for every morphism in the class there exists a palindrome such that is a first complete return word to for each…
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Taxonomy
Topicssemigroups and automata theory · Natural Language Processing Techniques · Authorship Attribution and Profiling
