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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000145
Mapping
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000145: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2,1,1] => [[2,2,2],[1,1]]
 => [1,1]
 => [1]
 => 0
[1,2,1,1] => [[2,2,2,1],[1,1]]
 => [1,1]
 => [1]
 => 0
[2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => -1
[2,1,2] => [[3,2,2],[1,1]]
 => [1,1]
 => [1]
 => 0
[2,2,1] => [[3,3,2],[2,1]]
 => [2,1]
 => [1]
 => 0
[3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => [1]
 => 0
[1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => -1
[1,2,1,2] => [[3,2,2,1],[1,1]]
 => [1,1]
 => [1]
 => 0
[1,2,2,1] => [[3,3,2,1],[2,1]]
 => [2,1]
 => [1]
 => 0
[1,3,1,1] => [[3,3,3,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,1]
 => -2
[2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => -1
[2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => -1
[2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => [1]
 => 0
[2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 0
[2,2,2] => [[4,3,2],[2,1]]
 => [2,1]
 => [1]
 => 0
[2,3,1] => [[4,4,2],[3,1]]
 => [3,1]
 => [1]
 => 0
[3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => [2,2,2]
 => [2,2]
 => 0
[3,1,2] => [[4,3,3],[2,2]]
 => [2,2]
 => [2]
 => 1
[3,2,1] => [[4,4,3],[3,2]]
 => [3,2]
 => [2]
 => 1
[4,1,1] => [[4,4,4],[3,3]]
 => [3,3]
 => [3]
 => 2
[1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]]
 => [1,1]
 => [1]
 => 0
[1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => -1
[1,1,2,1,2] => [[3,2,2,1,1],[1,1]]
 => [1,1]
 => [1]
 => 0
[1,1,2,2,1] => [[3,3,2,1,1],[2,1]]
 => [2,1]
 => [1]
 => 0
[1,1,3,1,1] => [[3,3,3,1,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,1]
 => -2
[1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => -1
[1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => -1
[1,2,1,3] => [[4,2,2,1],[1,1]]
 => [1,1]
 => [1]
 => 0
[1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 0
[1,2,2,2] => [[4,3,2,1],[2,1]]
 => [2,1]
 => [1]
 => 0
[1,2,3,1] => [[4,4,2,1],[3,1]]
 => [3,1]
 => [1]
 => 0
[1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]]
 => [2,2,2]
 => [2,2]
 => 0
[1,3,1,2] => [[4,3,3,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,3,2,1] => [[4,4,3,1],[3,2]]
 => [3,2]
 => [2]
 => 1
[1,4,1,1] => [[4,4,4,1],[3,3]]
 => [3,3]
 => [3]
 => 2
[2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => -3
[2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,1]
 => -2
[2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]]
 => [2,1,1,1]
 => [1,1,1]
 => -2
[2,1,1,3] => [[4,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => -1
[2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]]
 => [2,2,1,1]
 => [2,1,1]
 => -1
[2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => -1
[2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => [3,1,1]
 => [1,1]
 => -1
[2,1,4] => [[5,2,2],[1,1]]
 => [1,1]
 => [1]
 => 0
[2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]]
 => [2,2,2,1]
 => [2,2,1]
 => -1
[2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 0
[2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => [3,2,1]
 => [2,1]
 => 0
[2,2,3] => [[5,3,2],[2,1]]
 => [2,1]
 => [1]
 => 0
Description
The Dyson rank of a partition. This rank is defined as the largest part minus the number of parts. It was introduced by Dyson [1] in connection to Ramanujan's partition congruences p(5n+4) \equiv 0 \pmod 5 and p(7n+6) \equiv 0 \pmod 7.