Frid's conjecture on bounded palindromic length sequences
Frid's conjecture on bounded palindromic length sequences
For a finite word, its palindromic length is the minimum number of palindromes whose concatenation is the word. For an infinite word, its palindromic length sequence records the palindromic lengths of all its finite prefixes.
Frid's conjecture. The palindromic length sequence of an infinite word is bounded if and only if the infinite word is ultimately periodic.
This conjecture connects bounded palindromic complexity with eventual periodicity of infinite words. The supplied text attributes it to the cited authors but gives no evidence resolving it.
Sources & referencesView supporting material
Primary source
Shuo Li, “Palindromic length sequence of the ruler sequence and of the period-doubling sequence”, arXiv:2007.08317 (2020).
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