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

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Bibliographic Details
Title:	On a sequence of Kimberling and its relationship to the Tribonacci word.
Authors:	Dvořáková, Lubomíra¹, Pelantová, Edita¹, Shallit, Jeffrey²
Source:	Discrete Mathematics & Theoretical Computer Science (DMTCS). 2026, Vol. 28 Issue 2, p1-14. 14p.
Subjects:	Binary sequences, Critical exponents, Mathematics
Abstract:	In 2017, Clark Kimberling defined an interesting sequence B = 0100101100 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 factor complexity and critical exponent of B. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	In 2017, Clark Kimberling defined an interesting sequence B = 0100101100 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 factor complexity and critical exponent of B. [ABSTRACT FROM AUTHOR]
ISSN:	13658050