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%I #12 Mar 30 2023 09:16:24
%S 1,1,1,2,1,1,1,3,2,3,1,1,1,1,1,4,3,4,2,2,3,4,1,1,1,1,1,1,1,1,1,5,4,5,
%T 3,5,4,5,2,2,2,5,3,3,4,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6,5,6,4,6,
%U 5,6,3,3,5,6,4,6,5,6,2,2,2,2,2,2,5,6,3,3,3,3,4,4,5,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Length of largest (i.e., leftmost) Lyndon word in Lyndon factorization of binary vectors of lengths 1, 2, 3, ...
%C Any binary word has a unique factorization as a product of nonincreasing Lyndon words (see Lothaire). Here we look at the Lyndon factorizations of the binary vectors 0,1, 00,01,10,11, 000,001,010,011,100,101,110,111, 0000,...
%C See A211097, A211099, A211100 for further information, including Maple code.
%C The smallest (or rightmost) factors are given by A211095 and A211096, offset by 2.
%D M. Lothaire, Combinatorics on Words, Addison-Wesley, Reading, MA, 1983. See Theorem 5.1.5, p. 67.
%D G. Melançon, Factorizing infinite words using Maple, MapleTech Journal, vol. 4, no. 1, 1997, pp. 34-42
%H N. J. A. Sloane, <a href="/A211097/a211097.txt">Maple programs for A211097 etc.</a>
%e Here are the Lyndon factorizations of the first few binary vectors:
%e .0.
%e .1.
%e .0.0.
%e .01.
%e .1.0.
%e .1.1.
%e .0.0.0.
%e .001.
%e .01.0.
%e .011.
%e .1.0.0.
%e .1.01.
%e .1.1.0.
%e .1.1.1.
%e .0.0.0.0.
%e ...
%Y Cf. A001037 (number of Lyndon words of length m); A102659 (list thereof), A211100.
%Y Cf. A211095-A211099.
%K nonn
%O 1,4
%A _N. J. A. Sloane_, Apr 01 2012