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%I #13 Sep 22 2023 08:58:26
%S 1,2,1,1,3,1,2,1,1,1,4,1,3,2,2,1,1,2,1,1,1,1,5,1,4,2,3,1,1,3,1,2,2,1,
%T 1,1,2,1,1,1,1,1,6,1,5,2,4,1,1,4,3,3,1,2,3,1,1,1,3,2,2,2,1,1,2,2,1,1,
%U 1,1,2,1,1,1,1,1,1,7,1,6,2,5,1,1,5,3,4,1,2,4
%N Irregular triangle whose reversed rows are all integer partitions in graded reverse-lexicographic order.
%C First differs from A036036 for partitions of 6.
%C First differs from A334442 for partitions of 6.
%C Also reversed partitions in reverse-colexicographic order.
%H OEIS Wiki, <a href="http://oeis.org/wiki/Orderings of partitions">Orderings of partitions</a>
%H Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e The sequence of all reversed partitions begins:
%e () (1,1,3) (7) (8)
%e (1) (1,2,2) (1,6) (1,7)
%e (2) (1,1,1,2) (2,5) (2,6)
%e (1,1) (1,1,1,1,1) (1,1,5) (1,1,6)
%e (3) (6) (3,4) (3,5)
%e (1,2) (1,5) (1,2,4) (1,2,5)
%e (1,1,1) (2,4) (1,1,1,4) (1,1,1,5)
%e (4) (1,1,4) (1,3,3) (4,4)
%e (1,3) (3,3) (2,2,3) (1,3,4)
%e (2,2) (1,2,3) (1,1,2,3) (2,2,4)
%e (1,1,2) (1,1,1,3) (1,1,1,1,3) (1,1,2,4)
%e (1,1,1,1) (2,2,2) (1,2,2,2) (1,1,1,1,4)
%e (5) (1,1,2,2) (1,1,1,2,2) (2,3,3)
%e (1,4) (1,1,1,1,2) (1,1,1,1,1,2) (1,1,3,3)
%e (2,3) (1,1,1,1,1,1) (1,1,1,1,1,1,1) (1,2,2,3)
%e We have the following tetrangle of reversed partitions:
%e 0
%e (1)
%e (2)(11)
%e (3)(12)(111)
%e (4)(13)(22)(112)(1111)
%e (5)(14)(23)(113)(122)(1112)(11111)
%e (6)(15)(24)(114)(33)(123)(1113)(222)(1122)(11112)(111111)
%t revlexsort[f_,c_]:=OrderedQ[PadRight[{c,f}]];
%t Reverse/@Join@@Table[Sort[IntegerPartitions[n],revlexsort],{n,0,8}]
%Y Row lengths are A000041.
%Y The version for reversed partitions is A026792.
%Y The version for colex instead of revlex is A026791.
%Y The version for lex instead of revlex is A080576.
%Y The non-reflected version is A080577.
%Y The number of distinct parts is A115623.
%Y Taking Heinz numbers gives A129129.
%Y The version for compositions is A228351.
%Y Partition lengths are A238966.
%Y Partition maxima are A331581.
%Y The length-sensitive version is A334442.
%Y Lexicographically ordered partitions are A193073.
%Y Partitions in colexicographic order are A211992.
%Y Cf. A036036, A036037, A112798, A129129, A228531, A296774, A334301, A334302, A334435, A334436, A334438, A334439.
%K nonn,tabf
%O 0,2
%A _Gus Wiseman_, May 24 2020
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