On a sequence of Kimberling and its relationship to the Tribonacci word
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917374065639424 |
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| author | Dvořáková, Lubomíra Pelantová, Edita Shallit, Jeffrey |
| author_facet | Dvořáková, Lubomíra Pelantová, Edita Shallit, Jeffrey |
| contents | 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 $\bf B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a sequence of Kimberling and its relationship to the Tribonacci word Dvořáková, Lubomíra Pelantová, Edita Shallit, Jeffrey Combinatorics Formal Languages and Automata Theory 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 $\bf B$. |
| title | On a sequence of Kimberling and its relationship to the Tribonacci word |
| topic | Combinatorics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2510.11318 |