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A329318 List of co-Lyndon words on {1,2} sorted first by length and then lexicographically. 20
1, 2, 21, 211, 221, 2111, 2211, 2221, 21111, 21211, 22111, 22121, 22211, 22221, 211111, 212111, 221111, 221121, 221211, 222111, 222121, 222211, 222221, 2111111, 2112111, 2121111, 2121211, 2211111, 2211121, 2211211, 2212111, 2212121, 2212211, 2221111, 2221121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The co-Lyndon product of two or more finite sequences is defined to be the lexicographically minimal sequence obtainable by shuffling the sequences together. For example, the co-Lyndon product of (231) and (213) is (212313), the product of (221) and (213) is (212213), and the product of (122) and (2121) is (1212122). A co-Lyndon word is a finite sequence that is prime with respect to the co-Lyndon product. Equivalently, a co-Lyndon word is a finite sequence that is lexicographically strictly greater than all of its cyclic rotations. Every finite sequence has a unique (orderless) factorization into co-Lyndon words, and if these factors are arranged in a certain order, their concatenation is equal to their co-Lyndon product. For example, (1001) has sorted co-Lyndon factorization (1)(100).

LINKS

Table of n, a(n) for n=1..35.

MATHEMATICA

colynQ[q_]:=Array[Union[{RotateRight[q, #], q}]=={RotateRight[q, #], q}&, Length[q]-1, 1, And];

Join@@Table[FromDigits/@Select[Tuples[{1, 2}, n], colynQ], {n, 5}]

CROSSREFS

The non-"co" version is A102659.

Numbers whose binary expansion is co-Lyndon are A275692.

Length of the co-Lyndon factorization of the binary expansion is A329312.

Cf. A000031, A001037, A027375, A059966, A060223, A211100, A328596, A329324.

Sequence in context: A131584 A037736 A328073 * A037559 A042349 A037495

Adjacent sequences:  A329315 A329316 A329317 * A329319 A329320 A329321

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 11 2019

STATUS

approved

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Last modified September 26 02:28 EDT 2020. Contains 337346 sequences. (Running on oeis4.)