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Flattened tetrangle of reversed strict integer partitions, sorted first by length and then colexicographically.
8

%I #5 May 12 2021 06:43:57

%S 1,2,3,1,2,4,1,3,5,2,3,1,4,6,2,4,1,5,1,2,3,7,3,4,2,5,1,6,1,2,4,8,3,5,

%T 2,6,1,7,1,3,4,1,2,5,9,4,5,3,6,2,7,1,8,2,3,4,1,3,5,1,2,6,10,4,6,3,7,2,

%U 8,1,9,2,3,5,1,4,5,1,3,6,1,2,7,1,2,3,4

%N Flattened tetrangle of reversed strict integer partitions, sorted first by length and then colexicographically.

%C First differs from the revlex (instead of colex) version for partitions of 12.

%C The zeroth row contains only the empty partition.

%C A tetrangle is a sequence of finite triangles.

%H Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order"> Lexicographic and colexicographic order</a>

%e Tetrangle begins:

%e 0: ()

%e 1: (1)

%e 2: (2)

%e 3: (3)(12)

%e 4: (4)(13)

%e 5: (5)(23)(14)

%e 6: (6)(24)(15)(123)

%e 7: (7)(34)(25)(16)(124)

%e 8: (8)(35)(26)(17)(134)(125)

%e 9: (9)(45)(36)(27)(18)(234)(135)(126)

%t Table[Reverse/@Sort[Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,30}]

%Y Positions of first appearances are A015724 plus one.

%Y Taking lex instead of colex gives A026793 (non-reversed: A118457).

%Y Triangle sums are A066189.

%Y Reversing all partitions gives A344090.

%Y The non-strict version is A344091.

%Y A319247 sorts strict partitions by Heinz number.

%Y A329631 sorts reversed strict partitions by Heinz number.

%Y Cf. A005117, A014466, A209862, A325683, A325859.

%Y Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344087, A344088, A344089.

%Y Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.

%K nonn,tabf

%O 0,2

%A _Gus Wiseman_, May 12 2021