Existence of a nonrepetitive palindrome-free sequence avoiding two subsequences
Let an infinite sequence be a sequence whose terms are drawn from the four-letter alphabet . A sequence is nonrepetitive if it contains no contiguous block of the form for a nonempty finite word , and palindrome-free if it contains no nonempty palindromic contiguous block. It avoids the subsequences and if neither of these occurs as a subsequence.
Sequence existence conjecture. There exists an infinite sequence on four letters, and such that the sequence is nonrepetitive, palindrome-free and avoids the subsequences and .
The paper states that this conjecture was recently confirmed by Kozik, so the existence claim is resolved.
References
Primary source
Balázs Keszegh, Balázs Patkós and Xuding Zhu, “Nonrepetitive colorings of lexicographic product of graphs”, arXiv:1210.5607 (2013).
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