A356923 - OEIS

A356923

Irregular table read by rows: invertible necklaces on the alphabet {0,1} sorted by length then by lexicographic order of minimum presentation.

%I #14 Sep 26 2022 20:37:26

%S 0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,

%T 0,0,1,0,0,0,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,

%U 1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0

%N Irregular table read by rows: invertible necklaces on the alphabet {0,1} sorted by length then by lexicographic order of minimum presentation.

%C An invertible necklace on the alphabet {0,1} is an equivalence class of binary strings where two strings are considered the same if (1) one string can be rotated to form the other or (2) swapping the 0s and 1s in one string results in the other string.

%C There are A000013(n) rows of length n.

%e Table begins:

%e 0,

%e 0, 0,

%e 0, 1,

%e 0, 0, 0,

%e 0, 0, 1,

%e 0, 0, 0, 0,

%e 0, 0, 0, 1,

%e 0, 0, 1, 1,

%e 0, 1, 0, 1,

%e 0, 0, 0, 0, 0,

%e 0, 0, 0, 0, 1,

%e 0, 0, 0, 1, 1,

%e 0, 0, 1, 0, 1,

%e 0, 0, 0, 0, 0, 0,

%e 0, 0, 0, 0, 0, 1,

%e 0, 0, 0, 0, 1, 1,

%e 0, 0, 0, 1, 0, 1,

%e 0, 0, 0, 1, 1, 1,

%e 0, 0, 1, 0, 0, 1,

%e 0, 0, 1, 0, 1, 1,

%e 0, 1, 0, 1, 0, 1,

%e ...

%e "0,0,1,1,1" is not a a row in this table because 0,0,1,1,1 = 1,1,0,0,0 = 0,0,0,1,1 and 0,0,0,1,1 is lexicographically earlier.

%Y Cf. A000013.

%Y Cf. A356921 (necklaces), A356922 (bracelets), A356924 (invertible bracelets).

%K nonn,tabf

%O 1

%A _Peter Kagey_, Sep 04 2022