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Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in reverse-lexicographic order.
6

%I #5 Dec 19 2017 02:41:47

%S 1,2,3,1,2,4,1,3,1,1,2,5,2,3,1,4,1,2,2,1,1,3,1,1,1,2,6,2,4,1,5,1,3,2,

%T 1,2,3,1,1,4,1,1,2,2,1,1,1,3,1,1,1,1,2,7,3,4,2,5,2,2,3,1,6,1,4,2,1,3,

%U 3,1,2,4,1,2,2,2,1,2,1,3,1,1,5,1,1,3,2

%N Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in reverse-lexicographic order.

%F Row n is a concatenation of A059966(n) Lyndon words with total length A000740(n).

%e Triangle of Lyndon compositions begins:

%e (1),

%e (2),

%e (3),(12),

%e (4),(13),(112),

%e (5),(23),(14),(122),(113),(1112),

%e (6),(24),(15),(132),(123),(114),(1122),(1113),(11112),

%e (7),(34),(25),(223),(16),(142),(133),(124),(1222),(1213),(115),(1132),(1123),(11212),(1114),(11122),(11113),(111112).

%t LyndonQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And]&&Array[RotateRight[q,#]&,Length[q],1,UnsameQ];

%t Table[Sort[Select[Join@@Permutations/@IntegerPartitions[n],LyndonQ],OrderedQ[PadRight[{#2,#1}]]&],{n,7}]

%Y Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A294859, A296302, A296373.

%K nonn,tabf

%O 1,2

%A _Gus Wiseman_, Dec 18 2017