|
|
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
|
|
|
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
|
Numbers whose binary expansion is co-Lyndon are A275692.
Length of the co-Lyndon factorization of the binary expansion is A329312.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|