WELLDOC property for words generated by morphisms
Svetlana Puzynina, Vladimir Schavelev

TL;DR
This paper investigates the WELLDOC property, which concerns the distribution of factors in infinite words, and provides a criterion for when words generated by morphisms possess this property.
Contribution
It introduces a criterion to determine the WELLDOC property in infinite words produced by morphisms, expanding understanding of their combinatorial structure.
Findings
Characterization of the WELLDOC property for morphic words
Criterion for WELLDOC based on morphism properties
Application to specific classes of infinite words
Abstract
In this paper, we study an abelian-type property of infinite words called well distributed occurrences, or WELLDOC for short. An infinite word on a -ary alphabet has the WELLDOC property if, for each factor of , positive integer , and vector , there is an occurrence of such that the Parikh vector of the prefix of preceding such occurrence is congruent to modulo . The Parikh vector of a finite word on an alphabet has its -th component equal to the number of occurrences of the -th letter in . We provide a criterion of the WELLDOC property for words generated by morphisms.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Algorithms and Data Compression
