On a sequence of Kimberling and its relationship to the Tribonacci word
Combinatorics
2026-04-01 v5 Formal Languages and Automata Theory
Abstract
In 2017, Clark Kimberling defined an interesting sequence of 's and '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 .
Cite
@article{arxiv.2510.11318,
title = {On a sequence of Kimberling and its relationship to the Tribonacci word},
author = {Lubomíra Dvořáková and Edita Pelantová and Jeffrey Shallit},
journal= {arXiv preprint arXiv:2510.11318},
year = {2026}
}