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A342531
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Triangle read by rows where T(n,k) is the number of strict integer partitions of n with maximal descent k, n >= 0, 0 <= k <= n.
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0
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1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 2, 3, 1, 1, 1, 1, 0, 1, 0, 0
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OFFSET
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0,39
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COMMENTS
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The maximal descent of an empty or singleton partition is considered to be 0.
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LINKS
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EXAMPLE
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Triangle begins:
1
1 0
1 0 0
1 1 0 0
1 0 1 0 0
1 1 0 1 0 0
1 1 1 0 1 0 0
1 1 1 1 0 1 0 0
1 0 2 1 1 0 1 0 0
1 2 1 1 1 1 0 1 0 0
1 1 2 2 1 1 1 0 1 0 0
1 1 2 3 1 1 1 1 0 1 0 0
1 1 3 2 3 1 1 1 1 0 1 0 0
1 1 3 3 3 2 1 1 1 1 0 1 0 0
1 1 3 4 3 3 2 1 1 1 1 0 1 0 0
1 3 3 4 4 3 2 2 1 1 1 1 0 1 0 0
1 0 5 5 5 4 3 2 2 1 1 1 1 0 1 0 0
1 1 4 7 5 5 4 2 2 2 1 1 1 1 0 1 0 0
1 2 5 6 7 6 4 4 2 2 2 1 1 1 1 0 1 0 0
1 1 5 9 7 7 6 4 3 2 2 2 1 1 1 1 0 1 0 0
1 1 6 9 9 7 8 5 4 3 2 2 2 1 1 1 1 0 1 0 0
Row n = 15 counts the following strict partitions (empty columns indicated by dots, A..F = 10..15):
F 87 753 96 762 A5 A41 B4 B31 C3 C21 D2 . E1 . .
654 6432 852 843 861 9321 A32
54321 6531 7431 951 942
7521 8421
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&If[Length[#]<=1, k==0, Max[Differences[Reverse[#]]]==k]&]], {n, 0, 15}, {k, 0, n}]
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CROSSREFS
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A049980 counts strict partitions with equal differences.
A325325 counts partitions with distinct differences (ranking: A325368).
A325545 counts compositions with distinct differences.
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KEYWORD
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AUTHOR
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STATUS
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approved
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