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A332235
Least integer t such that every binary word of length t+1 contains an split occurrence of an n-overlap.
4
OFFSET
0,1
COMMENTS
An "n-overlap" is a word of the form xxx', where x is a nonempty word of length at least n, and x' is a prefix of x of length n. Thus, for example, abcdabcdab is a 2-overlap. A split occurrence of a pattern p is a word of the form xyz where xz matches the pattern.
For n = 0,1,2,3 the lexicographically least words achieving the bound are:
n = 0: 01
n = 1: 0011
n = 2: 000110100111
n = 3: 00111010100001010011101000011111000011010001110
LINKS
D. Gabric and J. Shallit, Avoidance of split overlaps, arxiv preprint arXiv:2002.01968 [cs.DM], February 5 2020.
CROSSREFS
Cf. A332234.
Sequence in context: A074449 A364622 A359328 * A131387 A207647 A152453
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Feb 07 2020
STATUS
approved