Work

On a sequence of Kimberling and its relationship to the Tribonacci word

Year: 2026

Type: article

Abstract: In 2017, Clark Kimberling defined an interesting sequence ${\bf B} = 0100101100 \cdots$ of $0$'s and $1$'s by certain inflation rules, and he made a number of conjectures about this sequence and some related ones. In this note we prove his conjectures using, in part, the Walnut theorem-prover. We show how his word is related to the infinite Tribonacci word, and we determine both the subword complexity and critical exponent of $\bf B$.

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.16926

Authors: Lubomíra Dvořáková, Edita Pelantová, Jeffrey Shallit

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Natural Sciences and Engineering Research Council of Canada

OpenAlex ID: W7140098269

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