OFFSET
1,2
COMMENTS
An abelian cube is three consecutive blocks x x' x'' of the same length and having the same number of occurrences of each letter. For example, "deeded" is an abelian cube. The order of an abelian cube x x' x'' is the length of x.
LINKS
C. F. Du, H. Mousavi, L. Schaeffer, and Jeffrey Shallit, Decision Algorithms for Fibonacci-Automatic Words, III: Enumeration and Abelian Properties, Intl. J. Found. Comput. Sci. 27 (2016), 943-963.
Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti, Additive word complexity and Walnut, arXiv:2410.02409 [math.CO], 2024. See p. 16.
EXAMPLE
For m = 1 neither 000 nor 111 appears in the Fibonacci word, so 1 is not a term.
But for m = 2 the word 101001 appears, so 2 is a term.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jul 23 2020
STATUS
approved