bibkey: frid2018sturmiannumeration authors: Anna E. Frid year: 2018 title: Sturmian numeration systems and decompositions to palindromes doi: 10.1016/j.ejc.2018.04.003 url: https://arxiv.org/abs/1710.11553v2 claim: Fibonacci and more general Sturmian numeration provide structural descriptions of palindrome occurrences and decompositions. strata_touched:

• D5/S1/Words/Palindromes/FridPrefix/FridUpper license: citation-only triage: anchor

Sturmian numeration systems and decompositions to palindromes

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European Journal of Combinatorics 71 (2018), pages 202–212. DOI: https://doi.org/10.1016/j.ejc.2018.04.003 Preprint version: https://arxiv.org/abs/1710.11553v2

Cited scope

The numeration-based palindrome analysis supplies context for the Fibonacci prefix family in Frid’s Numeration 2018 Conjecture 2. The conjecture’s exact source sentence, printed page 12 of the meeting abstract, is:

For every k ≥ 1, the prefix of the Fibonacci word of length (100)²ᵏ⁻¹101 cannot be decomposed as a concatenation of at most 2k palindromes.

The repository’s goldenWord uses true for the Fibonacci letter 0 and false for 1; this letter coding preserves palindrome decompositions.