login
Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in lexicographic order.
12

%I #22 Dec 19 2017 02:37:33

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

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

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

%N Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in 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 (12),(3),

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

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

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

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

%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[{#1,#2}]]&],{n,7}]

%Y Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A296302, A296373, A296656.

%K nonn,tabf

%O 1,2

%A _Gus Wiseman_, Dec 18 2017