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Matching statistic: St001251
St001251: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 0
[2]
=> 1
[1,1]
=> 0
[3]
=> 1
[2,1]
=> 1
[1,1,1]
=> 0
[4]
=> 0
[3,1]
=> 1
[2,2]
=> 2
[2,1,1]
=> 1
[1,1,1,1]
=> 0
[5]
=> 1
[4,1]
=> 0
[3,2]
=> 2
[3,1,1]
=> 1
[2,2,1]
=> 2
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 0
[6]
=> 1
[5,1]
=> 1
[4,2]
=> 1
[4,1,1]
=> 0
[3,3]
=> 2
[3,2,1]
=> 2
[3,1,1,1]
=> 1
[2,2,2]
=> 3
[2,2,1,1]
=> 2
[2,1,1,1,1]
=> 1
[1,1,1,1,1,1]
=> 0
[7]
=> 0
[6,1]
=> 1
[5,2]
=> 2
[5,1,1]
=> 1
[4,3]
=> 1
[4,2,1]
=> 1
[4,1,1,1]
=> 0
[3,3,1]
=> 2
[3,2,2]
=> 3
[3,2,1,1]
=> 2
[3,1,1,1,1]
=> 1
[2,2,2,1]
=> 3
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 0
[8]
=> 1
[7,1]
=> 0
[6,2]
=> 2
[6,1,1]
=> 1
[5,3]
=> 2
[5,2,1]
=> 2
Description
The number of parts of a partition that are not congruent 1 modulo 3.
Matching statistic: St001250
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001250: Integer partitions ⟶ ℤResult quality: 40% ●values known / values provided: 84%●distinct values known / distinct values provided: 40%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001250: Integer partitions ⟶ ℤResult quality: 40% ●values known / values provided: 84%●distinct values known / distinct values provided: 40%
Values
[1]
=> [1]
=> []
=> []
=> ? = 0
[2]
=> [1,1]
=> [1]
=> [1]
=> 1
[1,1]
=> [2]
=> []
=> []
=> ? = 0
[3]
=> [1,1,1]
=> [1,1]
=> [2]
=> 1
[2,1]
=> [2,1]
=> [1]
=> [1]
=> 1
[1,1,1]
=> [3]
=> []
=> []
=> ? = 0
[4]
=> [1,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[3,1]
=> [2,1,1]
=> [1,1]
=> [2]
=> 1
[2,2]
=> [2,2]
=> [2]
=> [1,1]
=> 2
[2,1,1]
=> [3,1]
=> [1]
=> [1]
=> 1
[1,1,1,1]
=> [4]
=> []
=> []
=> ? = 0
[5]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[4,1]
=> [2,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[3,2]
=> [2,2,1]
=> [2,1]
=> [2,1]
=> 2
[3,1,1]
=> [3,1,1]
=> [1,1]
=> [2]
=> 1
[2,2,1]
=> [3,2]
=> [2]
=> [1,1]
=> 2
[2,1,1,1]
=> [4,1]
=> [1]
=> [1]
=> 1
[1,1,1,1,1]
=> [5]
=> []
=> []
=> ? = 0
[6]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> 1
[5,1]
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[4,2]
=> [2,2,1,1]
=> [2,1,1]
=> [3,1]
=> 1
[4,1,1]
=> [3,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[3,3]
=> [2,2,2]
=> [2,2]
=> [2,2]
=> 2
[3,2,1]
=> [3,2,1]
=> [2,1]
=> [2,1]
=> 2
[3,1,1,1]
=> [4,1,1]
=> [1,1]
=> [2]
=> 1
[2,2,2]
=> [3,3]
=> [3]
=> [1,1,1]
=> 3
[2,2,1,1]
=> [4,2]
=> [2]
=> [1,1]
=> 2
[2,1,1,1,1]
=> [5,1]
=> [1]
=> [1]
=> 1
[1,1,1,1,1,1]
=> [6]
=> []
=> []
=> ? = 0
[7]
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [6]
=> 0
[6,1]
=> [2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> 1
[5,2]
=> [2,2,1,1,1]
=> [2,1,1,1]
=> [4,1]
=> 2
[5,1,1]
=> [3,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[4,3]
=> [2,2,2,1]
=> [2,2,1]
=> [3,2]
=> 1
[4,2,1]
=> [3,2,1,1]
=> [2,1,1]
=> [3,1]
=> 1
[4,1,1,1]
=> [4,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[3,3,1]
=> [3,2,2]
=> [2,2]
=> [2,2]
=> 2
[3,2,2]
=> [3,3,1]
=> [3,1]
=> [2,1,1]
=> 3
[3,2,1,1]
=> [4,2,1]
=> [2,1]
=> [2,1]
=> 2
[3,1,1,1,1]
=> [5,1,1]
=> [1,1]
=> [2]
=> 1
[2,2,2,1]
=> [4,3]
=> [3]
=> [1,1,1]
=> 3
[2,2,1,1,1]
=> [5,2]
=> [2]
=> [1,1]
=> 2
[2,1,1,1,1,1]
=> [6,1]
=> [1]
=> [1]
=> 1
[1,1,1,1,1,1,1]
=> [7]
=> []
=> []
=> ? = 0
[8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> [7]
=> 1
[7,1]
=> [2,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [6]
=> 0
[6,2]
=> [2,2,1,1,1,1]
=> [2,1,1,1,1]
=> [5,1]
=> 2
[6,1,1]
=> [3,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> 1
[5,3]
=> [2,2,2,1,1]
=> [2,2,1,1]
=> [4,2]
=> 2
[5,2,1]
=> [3,2,1,1,1]
=> [2,1,1,1]
=> [4,1]
=> 2
[5,1,1,1]
=> [4,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[4,4]
=> [2,2,2,2]
=> [2,2,2]
=> [3,3]
=> 0
[4,3,1]
=> [3,2,2,1]
=> [2,2,1]
=> [3,2]
=> 1
[4,2,2]
=> [3,3,1,1]
=> [3,1,1]
=> [3,1,1]
=> 2
[4,2,1,1]
=> [4,2,1,1]
=> [2,1,1]
=> [3,1]
=> 1
[4,1,1,1,1]
=> [5,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[3,3,2]
=> [3,3,2]
=> [3,2]
=> [2,2,1]
=> 3
[1,1,1,1,1,1,1,1]
=> [8]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1]
=> [9]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1]
=> [10]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1,1]
=> [11]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1,1,1]
=> [12]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [13]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [14]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [15]
=> []
=> []
=> ? = 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [16]
=> []
=> []
=> ? = 0
[]
=> []
=> ?
=> ?
=> ? = 0
[7,6,5,4,3,2,1]
=> [7,6,5,4,3,2,1]
=> [6,5,4,3,2,1]
=> [6,5,4,3,2,1]
=> ? = 4
[6,6,5,4,3,2,1]
=> [7,6,5,4,3,2]
=> [6,5,4,3,2]
=> [5,5,4,3,2,1]
=> ? = 5
[6,5,5,4,3,2,1]
=> [7,6,5,4,3,1]
=> [6,5,4,3,1]
=> [5,4,4,3,2,1]
=> ? = 5
[5,5,5,4,3,2,1]
=> [7,6,5,4,3]
=> [6,5,4,3]
=> [4,4,4,3,2,1]
=> ? = 5
[6,5,4,4,3,2,1]
=> [7,6,5,4,2,1]
=> [6,5,4,2,1]
=> [5,4,3,3,2,1]
=> ? = 4
[7,6,5,4,3,2]
=> [6,6,5,4,3,2,1]
=> [6,5,4,3,2,1]
=> [6,5,4,3,2,1]
=> ? = 4
[7,6,2,2,2,2]
=> [6,6,2,2,2,2,1]
=> ?
=> ?
=> ? = 5
[4,4,4,4,3]
=> [5,5,5,4]
=> ?
=> ?
=> ? = 1
[4,4,4,3,3]
=> ?
=> ?
=> ?
=> ? = 2
[4,4,4,4,2]
=> [5,5,4,4]
=> ?
=> ?
=> ? = 1
[6,6,5,4]
=> [4,4,4,4,3,2]
=> ?
=> ?
=> ? = 3
[6,4,4,4]
=> [4,4,4,4,1,1]
=> ?
=> ?
=> ? = 1
[2,2,2,2,2,2,2,2,2,2]
=> ?
=> ?
=> ?
=> ? = 10
[3,3,3,3,3,3,2]
=> ?
=> ?
=> ?
=> ? = 7
[4,4,3,3,3,3]
=> ?
=> ?
=> ?
=> ? = 4
[3,3,3,3,3,3,3,3,3]
=> ?
=> ?
=> ?
=> ? = 9
[4,4,4,4,3,3]
=> ?
=> ?
=> ?
=> ? = 2
[4,4,4,3,3,3]
=> [6,6,6,3]
=> ?
=> ?
=> ? = 3
[4,4,4,4,4,4]
=> [6,6,6,6]
=> [6,6,6]
=> [3,3,3,3,3,3]
=> ? = 0
[4,4,4,4,4,4,4,4]
=> ?
=> ?
=> ?
=> ? = 0
[18]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ?
=> ?
=> ? = 1
[19]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ?
=> ?
=> ? = 0
[20]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ?
=> ?
=> ? = 1
[21]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ?
=> ?
=> ? = 1
[6,6,6,6]
=> [4,4,4,4,4,4]
=> [4,4,4,4,4]
=> [5,5,5,5]
=> ? = 4
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> [16,16,1]
=> ?
=> ?
=> ? = 16
[7,6,6,6]
=> [4,4,4,4,4,4,1]
=> ?
=> ?
=> ? = 3
[7,2,2,2,2,2,2]
=> [7,7,1,1,1,1,1]
=> ?
=> ?
=> ? = 6
[4,2,2,2,2,2,2,2]
=> [8,8,1,1]
=> ?
=> ?
=> ? = 7
[10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> [2,2,2,2,2,2,2,2,2]
=> [9,9]
=> ? = 0
[6,6,6,6,6]
=> [5,5,5,5,5,5]
=> [5,5,5,5,5]
=> [5,5,5,5,5]
=> ? = 5
[11,7,3]
=> [3,3,3,2,2,2,2,1,1,1,1]
=> ?
=> ?
=> ? = 2
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> [32,32,1]
=> ?
=> ?
=> ? = 32
Description
The number of parts of a partition that are not congruent 0 modulo 3.
Matching statistic: St001232
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 23%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 23%
Values
[1]
=> [1]
=> [1,0]
=> [1,0]
=> 0
[2]
=> [1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[1,1]
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> ? = 1
[2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[1,1,1]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[4]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 0
[3,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 1
[2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
[2,1,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[1,1,1,1]
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[5]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[4,1]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 0
[3,2]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2
[3,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? = 1
[2,2,1]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,1,1,1]
=> [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
[1,1,1,1,1]
=> [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0
[6]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[5,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 1
[4,2]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1
[4,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 0
[3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? = 2
[3,2,1]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2
[3,1,1,1]
=> [4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 1
[2,2,2]
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,2,1,1]
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
[2,1,1,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[1,1,1,1,1,1]
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[7]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0
[6,1]
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[5,2]
=> [2,2,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 2
[5,1,1]
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> ? = 1
[4,3]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? = 1
[4,2,1]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> ? = 1
[4,1,1,1]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> ? = 0
[3,3,1]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? = 2
[3,2,2]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? = 3
[3,2,1,1]
=> [4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> ? = 2
[3,1,1,1,1]
=> [5,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 1
[2,2,2,1]
=> [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[2,2,1,1,1]
=> [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
[2,1,1,1,1,1]
=> [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
[1,1,1,1,1,1,1]
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 0
[8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[7,1]
=> [2,1,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0
[6,2]
=> [2,2,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2
[6,1,1]
=> [3,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[5,3]
=> [2,2,2,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ? = 2
[5,2,1]
=> [3,2,1,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=> ? = 2
[5,1,1,1]
=> [4,1,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
=> ? = 1
[4,4]
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? = 0
[4,3,1]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> ? = 1
[4,2,2]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> ? = 2
[4,2,1,1]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> ? = 1
[4,1,1,1,1]
=> [5,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
=> ? = 0
[3,3,2]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? = 3
[3,3,1,1]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> ? = 2
[3,2,2,1]
=> [4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 3
[3,2,1,1,1]
=> [5,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
=> ? = 2
[3,1,1,1,1,1]
=> [6,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
=> ? = 1
[2,2,2,2]
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[2,2,2,1,1]
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
[2,2,1,1,1,1]
=> [6,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
[2,1,1,1,1,1,1]
=> [7,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> ? = 1
[1,1,1,1,1,1,1,1]
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 0
[9]
=> [1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[8,1]
=> [2,1,1,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[7,2]
=> [2,2,1,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1
[7,1,1]
=> [3,1,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 0
[6,3]
=> [2,2,2,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 2
[6,2,1]
=> [3,2,1,1,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2
[2,2,2,2,1]
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
[2,2,2,1,1,1]
=> [6,3]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3
[2,2,2,2,2]
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
[2,2,2,2,1,1]
=> [6,4]
=> [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 4
[2,2,2,2,2,1]
=> [6,5]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 5
[2,2,2,2,2,2]
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 6
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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