OFFSET
0,2
COMMENTS
LINKS
OEIS Wiki, Orderings of partitions
Wikiversity, Lexicographic and colexicographic order
EXAMPLE
The sequence of all reversed partitions begins:
() (1,1,3) (7) (8)
(1) (1,2,2) (1,6) (1,7)
(2) (1,1,1,2) (2,5) (2,6)
(1,1) (1,1,1,1,1) (1,1,5) (1,1,6)
(3) (6) (3,4) (3,5)
(1,2) (1,5) (1,2,4) (1,2,5)
(1,1,1) (2,4) (1,1,1,4) (1,1,1,5)
(4) (1,1,4) (1,3,3) (4,4)
(1,3) (3,3) (2,2,3) (1,3,4)
(2,2) (1,2,3) (1,1,2,3) (2,2,4)
(1,1,2) (1,1,1,3) (1,1,1,1,3) (1,1,2,4)
(1,1,1,1) (2,2,2) (1,2,2,2) (1,1,1,1,4)
(5) (1,1,2,2) (1,1,1,2,2) (2,3,3)
(1,4) (1,1,1,1,2) (1,1,1,1,1,2) (1,1,3,3)
(2,3) (1,1,1,1,1,1) (1,1,1,1,1,1,1) (1,2,2,3)
We have the following tetrangle of reversed partitions:
0
(1)
(2)(11)
(3)(12)(111)
(4)(13)(22)(112)(1111)
(5)(14)(23)(113)(122)(1112)(11111)
(6)(15)(24)(114)(33)(123)(1113)(222)(1122)(11112)(111111)
MATHEMATICA
revlexsort[f_, c_]:=OrderedQ[PadRight[{c, f}]];
Reverse/@Join@@Table[Sort[IntegerPartitions[n], revlexsort], {n, 0, 8}]
CROSSREFS
Row lengths are A000041.
The version for reversed partitions is A026792.
The version for colex instead of revlex is A026791.
The version for lex instead of revlex is A080576.
The non-reflected version is A080577.
The number of distinct parts is A115623.
Taking Heinz numbers gives A129129.
The version for compositions is A228351.
Partition lengths are A238966.
Partition maxima are A331581.
The length-sensitive version is A334442.
Lexicographically ordered partitions are A193073.
Partitions in colexicographic order are A211992.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 24 2020
STATUS
approved