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A296656
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Triangle whose n-th row is the concatenated sequence of all Lyndon compositions of n in reverse-lexicographic order.
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6
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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, 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, 3, 1, 2, 4, 1, 2, 2, 2, 1, 2, 1, 3, 1, 1, 5, 1, 1, 3, 2
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OFFSET
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1,2
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LINKS
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FORMULA
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Row n is a concatenation of A059966(n) Lyndon words with total length A000740(n).
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EXAMPLE
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Triangle of Lyndon compositions begins:
(1),
(2),
(3),(12),
(4),(13),(112),
(5),(23),(14),(122),(113),(1112),
(6),(24),(15),(132),(123),(114),(1122),(1113),(11112),
(7),(34),(25),(223),(16),(142),(133),(124),(1222),(1213),(115),(1132),(1123),(11212),(1114),(11122),(11113),(111112).
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MATHEMATICA
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LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
Table[Sort[Select[Join@@Permutations/@IntegerPartitions[n], LyndonQ], OrderedQ[PadRight[{#2, #1}]]&], {n, 7}]
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CROSSREFS
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Cf. A000740, A001037, A001045, A008965, A059966, A060223, A066099, A101211, A102659, A124734, A185700, A228369, A281013, A294859, A296302, A296373.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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