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A080576
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Triangle in which n-th row lists all partitions of n, in graded reflected lexicographic order.
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19
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1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 2, 3, 1, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 3, 1, 2, 3, 3, 3, 1, 1, 4, 2, 4, 1, 5, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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COMMENTS
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The graded reflected lexicographic ordering of the partitions is used by Maple. - Daniel Forgues, Jan 19 2011
Each partition here is the conjugate of the corresponding partition in Abramowitz and Stegun order (A036036). The partitions are in the reverse of the order of the partitions in Mathematica order (A080577). - Franklin T. Adams-Watters, Oct 18 2006
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LINKS
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Alois P. Heinz, Rows n = 1..20, flattened
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. (uses Flash)
A. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions
OEIS Wiki, Orderings of partitions (a comparison).
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EXAMPLE
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First five rows are:
[[1]]
[[1, 1], [2]]
[[1, 1, 1], [1, 2], [3]]
[[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4]]
[[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [1, 1, 3], [2, 3], [1, 4], [5]]
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MAPLE
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with(combinat); partition(6);
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MATHEMATICA
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row[n_] := Flatten[Reverse /@ Reverse[SplitBy[Reverse /@ IntegerPartitions[n], Length]], 1]; Array[row, 7] // Flatten (* Jean-François Alcover, Dec 05 2016 *)
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CROSSREFS
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See A080577 for the Mathematica (graded reverse lexicographic) ordering.
See A036036 for the Hindenburg (graded reflected colexicographic) ordering (listed in the Abramowitz and Stegun Handbook).
See A036037 for the graded colexicographic ordering.
See A193073 for the graded lexicographic ordering. - M. F. Hasler, Jul 16 2011
See A228100 for the Fenner-Loizou (binary tree) ordering.
Sequence in context: A104758 A143227 A026791 * A213211 A194673 A240595
Adjacent sequences: A080573 A080574 A080575 * A080577 A080578 A080579
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, Mar 23 2003
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EXTENSIONS
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Edited by Daniel Forgues, Jan 21 2011
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STATUS
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approved
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