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%I #11 Sep 22 2023 08:47:51
%S 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,
%T 2,3,3,4,3,4,4,5,5,6,7,1,2,2,2,3,3,4,2,3,3,4,3,4,4,5,4,5,5,6,6,7,8,1,
%U 2,2,3,2,3,3,4,2,3,3,3,4,4,5,3,4,4,5,4,5,5,6,5,6,6,7,7,8,9
%N Length of the n-th reversed integer partition in graded reverse-lexicographic order. Partition lengths of A228531.
%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 Triangle begins:
%e 0
%e 1
%e 1 2
%e 1 2 3
%e 1 2 2 3 4
%e 1 2 2 3 3 4 5
%e 1 2 2 3 2 3 3 4 4 5 6
%e 1 2 2 3 2 3 3 4 3 4 4 5 5 6 7
%e 1 2 2 2 3 3 4 2 3 3 4 3 4 4 5 4 5 5 6 6 7 8
%t revlexsort[f_,c_]:=OrderedQ[PadRight[{c,f}]];
%t Table[Length/@Sort[Reverse/@IntegerPartitions[n],revlexsort],{n,0,8}]
%Y Row lengths are A000041.
%Y The generalization to compositions is A000120.
%Y Row sums are A006128.
%Y The same partition has sum A036042.
%Y The length-sensitive version (sum/length/revlex) is A036043.
%Y The colexicographic version (sum/colex) is A049085.
%Y The same partition has minimum A182715.
%Y The lexicographic version (sum/lex) is A193173.
%Y The tetrangle of these partitions is A228531.
%Y The version for non-reversed partitions is A238966.
%Y The same partition has Heinz number A334436.
%Y Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.
%Y Partitions in lexicographic order (sum/lex) are A193073.
%Y Partitions in colexicographic order (sum/colex) are A211992.
%Y Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.
%Y Cf. A026792, A049085, A080576, A080577, A103921, A112798, A115623, A129129, A331581, A334302, A334435, A334442.
%K nonn,tabf
%O 0,4
%A _Gus Wiseman_, May 23 2020
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