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A331581
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Maximum part of the n-th integer partition in graded reverse-lexicographic order (A080577); a(1) = 0.
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11
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0, 1, 2, 1, 3, 2, 1, 4, 3, 2, 2, 1, 5, 4, 3, 3, 2, 2, 1, 6, 5, 4, 4, 3, 3, 3, 2, 2, 2, 1, 7, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 1, 8, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 9, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1
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OFFSET
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1,3
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COMMENTS
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The first partition ranked by A080577 is (); there is no zeroth partition.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of all partitions in graded reverse-lexicographic order begins as follows. The terms are the initial parts.
() (3,2) (2,1,1,1,1) (2,2,1,1,1)
(1) (3,1,1) (1,1,1,1,1,1) (2,1,1,1,1,1)
(2) (2,2,1) (7) (1,1,1,1,1,1,1)
(1,1) (2,1,1,1) (6,1) (8)
(3) (1,1,1,1,1) (5,2) (7,1)
(2,1) (6) (5,1,1) (6,2)
(1,1,1) (5,1) (4,3) (6,1,1)
(4) (4,2) (4,2,1) (5,3)
(3,1) (4,1,1) (4,1,1,1) (5,2,1)
(2,2) (3,3) (3,3,1) (5,1,1,1)
(2,1,1) (3,2,1) (3,2,2) (4,4)
(1,1,1,1) (3,1,1,1) (3,2,1,1) (4,3,1)
(5) (2,2,2) (3,1,1,1,1) (4,2,2)
(4,1) (2,2,1,1) (2,2,2,1) (4,2,1,1)
Triangle begins:
0
1
2 1
3 2 1
4 3 2 2 1
5 4 3 3 2 2 1
6 5 4 4 3 3 3 2 2 2 1
7 6 5 5 4 4 4 3 3 3 3 2 2 2 1
8 7 6 6 5 5 5 4 4 4 4 4 3 3 3 3 3 2 2 2 2 1
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MATHEMATICA
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revlexsort[f_, c_]:=OrderedQ[PadRight[{c, f}]];
Prepend[First/@Join@@Table[Sort[IntegerPartitions[n], revlexsort], {n, 8}], 0]
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CROSSREFS
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Lexicographically ordered reversed partitions are A026791.
Reverse-colexicographically ordered partitions are A026792.
Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.
Reverse-lexicographically ordered partitions are A080577.
Distinct parts of these partitions are counted by A115623.
Lexicographically ordered partitions are A193073.
Colexicographically ordered partitions are A211992.
Lengths of these partitions are A238966.
Cf. A036037, A048793, A063008, A066099, A129129, A185974, A228100, A228531, A334301, A334434, A334436, A334438.
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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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