A321252 (Conjecturally) the lexicographically earliest infinite sequence over {0,1,2,3} avoiding abelian squares.

0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 1, 0, 1, 3, 1, 0, 1, 2, 1, 3, 2, 0, 2, 1, 0, 1, 3, 0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 2, 0, 2, 3, 1, 0, 1, 2, 0, 2, 3, 2, 0, 2, 1, 2, 3, 0, 3, 2, 3, 0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 2, 1, 3, 0, 1, 0, 2, 0, 3, 0, 1, 3, 0, 3, 2

Offset: 1

Author

Jeffrey Shallit, Nov 01 2018

Keywords

• nonn

Comments

An abelian square is a nonempty string where the second half is a rearrangement of the first half, like the English word "reappear". To "avoid" an abelian square means to have no contiguous block of that form. Although an easy compactness argument, combined with a result of Keränen (1992) shows that the lexicographically earliest infinite string avoiding abelian squares over the alphabet {0,1,2,3} must exist, the terms provided are only conjecturally part of the described sequence, because we have no proof currently that this particular string can be extended infinitely far to the right.

Links

• Veikko Keränen, Abelian squares are avoidable on 4 letters, in ICALP 1992, volume 623 of Lecture Notes in Comput. Sci., pages 41-52. Springer-Verlag, 1992.

Crossrefs

Cf. A272653, A272654, A272655.