WELLDOC property for words generated by morphisms

2026/03/09 by Svetlana Puzynina, Vladimir Schavelev · 1 voice
Computer Science · Mathematics · #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.2603.08492

Abstract

In this paper, we study an abelian-type property of infinite words called well distributed occurrences, or WELLDOC for short. An infinite word w on a d-ary alphabet has the WELLDOC property if, for each factor u of w, positive integer m, and vector v∈ ℕ^d, there is an occurrence of u such that the Parikh vector of the prefix of w preceding such occurrence is congruent to v modulo m. The Parikh vector of a finite word v on an alphabet has its i-th component equal to the number of occurrences of the i-th letter in v. We provide a criterion of the WELLDOC property for words generated by morphisms.

Citations

• Aperiodic pseudorandom number generators based on infinite words
• Decidability of uniform recurrence of morphic sequences
• Episturmian words: a survey

Discussions

• Svetlana Puzynina, Vladimir Schavelev: WELLDOC property for words generated by morphisms https://arxiv.org/abs/2603.08492 https://arxiv.org/pdf/2603.08492 https://arxiv.org/html/2603.08492 [bsky, 0 points, 0 comments]

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