OFFSET
0,4
LINKS
OEIS Wiki, Orderings of partitions
Wikiversity, Lexicographic and colexicographic order
EXAMPLE
Triangle begins:
0
1
1 2
1 2 3
1 2 2 3 4
1 2 2 3 3 4 5
1 2 2 3 2 3 3 4 4 5 6
1 2 2 3 2 3 3 4 3 4 4 5 5 6 7
1 2 2 2 3 3 4 2 3 3 4 3 4 4 5 4 5 5 6 6 7 8
MATHEMATICA
revlexsort[f_, c_]:=OrderedQ[PadRight[{c, f}]];
Table[Length/@Sort[Reverse/@IntegerPartitions[n], revlexsort], {n, 0, 8}]
CROSSREFS
Row lengths are A000041.
The generalization to compositions is A000120.
Row sums are A006128.
The same partition has sum A036042.
The length-sensitive version (sum/length/revlex) is A036043.
The colexicographic version (sum/colex) is A049085.
The same partition has minimum A182715.
The lexicographic version (sum/lex) is A193173.
The tetrangle of these partitions is A228531.
The version for non-reversed partitions is A238966.
The same partition has Heinz number A334436.
Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.
Partitions in lexicographic order (sum/lex) are A193073.
Partitions in colexicographic order (sum/colex) are A211992.
Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 23 2020
STATUS
approved