Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001250
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001250: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1]
 => [1]
 => [1]
 => 1
[2,1]
 => [1]
 => [1]
 => 1
[1,1,1]
 => [1,1]
 => [2]
 => 1
[3,1]
 => [1]
 => [1]
 => 1
[2,2]
 => [2]
 => [1,1]
 => 2
[2,1,1]
 => [1,1]
 => [2]
 => 1
[1,1,1,1]
 => [1,1,1]
 => [3]
 => 0
[4,1]
 => [1]
 => [1]
 => 1
[3,2]
 => [2]
 => [1,1]
 => 2
[3,1,1]
 => [1,1]
 => [2]
 => 1
[2,2,1]
 => [2,1]
 => [2,1]
 => 2
[2,1,1,1]
 => [1,1,1]
 => [3]
 => 0
[1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
[5,1]
 => [1]
 => [1]
 => 1
[4,2]
 => [2]
 => [1,1]
 => 2
[4,1,1]
 => [1,1]
 => [2]
 => 1
[3,3]
 => [3]
 => [1,1,1]
 => 3
[3,2,1]
 => [2,1]
 => [2,1]
 => 2
[3,1,1,1]
 => [1,1,1]
 => [3]
 => 0
[2,2,2]
 => [2,2]
 => [2,2]
 => 2
[2,2,1,1]
 => [2,1,1]
 => [3,1]
 => 1
[2,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
[1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 1
[6,1]
 => [1]
 => [1]
 => 1
[5,2]
 => [2]
 => [1,1]
 => 2
[5,1,1]
 => [1,1]
 => [2]
 => 1
[4,3]
 => [3]
 => [1,1,1]
 => 3
[4,2,1]
 => [2,1]
 => [2,1]
 => 2
[4,1,1,1]
 => [1,1,1]
 => [3]
 => 0
[3,3,1]
 => [3,1]
 => [2,1,1]
 => 3
[3,2,2]
 => [2,2]
 => [2,2]
 => 2
[3,2,1,1]
 => [2,1,1]
 => [3,1]
 => 1
[3,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
[2,2,2,1]
 => [2,2,1]
 => [3,2]
 => 1
[2,2,1,1,1]
 => [2,1,1,1]
 => [4,1]
 => 2
[2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 1
[1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [6]
 => 0
[7,1]
 => [1]
 => [1]
 => 1
[6,2]
 => [2]
 => [1,1]
 => 2
[6,1,1]
 => [1,1]
 => [2]
 => 1
[5,3]
 => [3]
 => [1,1,1]
 => 3
[5,2,1]
 => [2,1]
 => [2,1]
 => 2
[5,1,1,1]
 => [1,1,1]
 => [3]
 => 0
[4,4]
 => [4]
 => [1,1,1,1]
 => 4
[4,3,1]
 => [3,1]
 => [2,1,1]
 => 3
[4,2,2]
 => [2,2]
 => [2,2]
 => 2
[4,2,1,1]
 => [2,1,1]
 => [3,1]
 => 1
[4,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 1
[3,3,2]
 => [3,2]
 => [2,2,1]
 => 3
[3,3,1,1]
 => [3,1,1]
 => [3,1,1]
 => 2
Description
The number of parts of a partition that are not congruent 0 modulo 3.
Matching statistic: St001251
Mapping
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001251: Integer partitions ⟶ ℤResult quality: 85% ●values known / values provided: 89%●distinct values known / distinct values provided: 85%
Values
[1,1]
 => [2]
 => 1
[2,1]
 => [2,1]
 => 1
[1,1,1]
 => [3]
 => 1
[3,1]
 => [2,1,1]
 => 1
[2,2]
 => [2,2]
 => 2
[2,1,1]
 => [3,1]
 => 1
[1,1,1,1]
 => [4]
 => 0
[4,1]
 => [2,1,1,1]
 => 1
[3,2]
 => [2,2,1]
 => 2
[3,1,1]
 => [3,1,1]
 => 1
[2,2,1]
 => [3,2]
 => 2
[2,1,1,1]
 => [4,1]
 => 0
[1,1,1,1,1]
 => [5]
 => 1
[5,1]
 => [2,1,1,1,1]
 => 1
[4,2]
 => [2,2,1,1]
 => 2
[4,1,1]
 => [3,1,1,1]
 => 1
[3,3]
 => [2,2,2]
 => 3
[3,2,1]
 => [3,2,1]
 => 2
[3,1,1,1]
 => [4,1,1]
 => 0
[2,2,2]
 => [3,3]
 => 2
[2,2,1,1]
 => [4,2]
 => 1
[2,1,1,1,1]
 => [5,1]
 => 1
[1,1,1,1,1,1]
 => [6]
 => 1
[6,1]
 => [2,1,1,1,1,1]
 => 1
[5,2]
 => [2,2,1,1,1]
 => 2
[5,1,1]
 => [3,1,1,1,1]
 => 1
[4,3]
 => [2,2,2,1]
 => 3
[4,2,1]
 => [3,2,1,1]
 => 2
[4,1,1,1]
 => [4,1,1,1]
 => 0
[3,3,1]
 => [3,2,2]
 => 3
[3,2,2]
 => [3,3,1]
 => 2
[3,2,1,1]
 => [4,2,1]
 => 1
[3,1,1,1,1]
 => [5,1,1]
 => 1
[2,2,2,1]
 => [4,3]
 => 1
[2,2,1,1,1]
 => [5,2]
 => 2
[2,1,1,1,1,1]
 => [6,1]
 => 1
[1,1,1,1,1,1,1]
 => [7]
 => 0
[7,1]
 => [2,1,1,1,1,1,1]
 => 1
[6,2]
 => [2,2,1,1,1,1]
 => 2
[6,1,1]
 => [3,1,1,1,1,1]
 => 1
[5,3]
 => [2,2,2,1,1]
 => 3
[5,2,1]
 => [3,2,1,1,1]
 => 2
[5,1,1,1]
 => [4,1,1,1,1]
 => 0
[4,4]
 => [2,2,2,2]
 => 4
[4,3,1]
 => [3,2,2,1]
 => 3
[4,2,2]
 => [3,3,1,1]
 => 2
[4,2,1,1]
 => [4,2,1,1]
 => 1
[4,1,1,1,1]
 => [5,1,1,1]
 => 1
[3,3,2]
 => [3,3,2]
 => 3
[3,3,1,1]
 => [4,2,2]
 => 2
[16,1]
 => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => ? = 1
[15,2]
 => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]
 => ? = 2
[14,3]
 => [2,2,2,1,1,1,1,1,1,1,1,1,1,1]
 => ? = 3
[14,2,1]
 => [3,2,1,1,1,1,1,1,1,1,1,1,1,1]
 => ? = 2
[13,4]
 => [2,2,2,2,1,1,1,1,1,1,1,1,1]
 => ? = 4
[12,5]
 => [2,2,2,2,2,1,1,1,1,1,1,1]
 => ? = 5
[11,6]
 => [2,2,2,2,2,2,1,1,1,1,1]
 => ? = 6
[10,7]
 => [2,2,2,2,2,2,2,1,1,1]
 => ? = 7
[9,8]
 => [2,2,2,2,2,2,2,2,1]
 => ? = 8
[6,4,3,3,2,1]
 => [6,5,4,2,1,1]
 => ? = 3
[5,4,3,3,2,1]
 => [6,5,4,2,1]
 => ? = 3
[5,4,4,2,2,1]
 => [6,5,3,3,1]
 => ? = 4
[6,5,3,2,2,1]
 => [6,5,3,2,2,1]
 => ? = 5
[5,5,3,2,2,1]
 => [6,5,3,2,2]
 => ? = 5
[6,4,3,2,2,1]
 => [6,5,3,2,1,1]
 => ? = 4
[5,4,4,3,1,1]
 => [6,4,4,3,1]
 => ? = 2
[6,4,3,3,1,1]
 => [6,4,4,2,1,1]
 => ? = 2
[6,5,4,2,1,1]
 => [6,4,3,3,2,1]
 => ? = 4
[5,5,4,2,1,1]
 => [6,4,3,3,2]
 => ? = 4
[6,4,4,2,1,1]
 => [6,4,3,3,1,1]
 => ? = 3
[6,5,3,2,1,1]
 => [6,4,3,2,2,1]
 => ? = 4
[5,4,4,3,2]
 => [5,5,4,3,1]
 => ? = 3
[6,4,3,3,2]
 => [5,5,4,2,1,1]
 => ? = 3
[6,5,3,2,2]
 => [5,5,3,2,2,1]
 => ? = 5
[5,5,4,3,1]
 => [5,4,4,3,2]
 => ? = 3
[6,4,4,3,1]
 => [5,4,4,3,1,1]
 => ? = 2
[6,5,3,3,1]
 => [5,4,4,2,2,1]
 => ? = 3
[6,5,3,3,3,2,1]
 => [7,6,5,2,2,1]
 => ? = 4
[6,4,3,3,3,2,1]
 => [7,6,5,2,1,1]
 => ? = 3
[5,4,3,3,3,2,1]
 => ?
 => ? = 3
[6,3,3,3,3,2,1]
 => [7,6,5,1,1,1]
 => ? = 2
[3,3,3,3,3,2,1]
 => [7,6,5]
 => ? = 2
[6,5,4,3,2,2,1]
 => [7,6,4,3,2,1]
 => ? = 3
[5,5,4,3,2,2,1]
 => ?
 => ? = 3
[6,5,4,2,2,2,1]
 => [7,6,3,3,2,1]
 => ? = 4
[6,5,3,2,2,2,1]
 => [7,6,3,2,2,1]
 => ? = 4
[6,4,3,2,2,2,1]
 => [7,6,3,2,1,1]
 => ? = 3
[5,4,3,2,2,2,1]
 => ?
 => ? = 3
[6,5,2,2,2,2,1]
 => [7,6,2,2,2,1]
 => ? = 4
[7,2,2,2,2,2,1]
 => [7,6,1,1,1,1,1]
 => ? = 1
[4,4,4,4,2,1,1]
 => [7,5,4,4]
 => ? = 1
[6,5,4,3,2,1,1]
 => [7,5,4,3,2,1]
 => ? = 3
[5,5,4,3,2,1,1]
 => [7,5,4,3,2]
 => ? = 3
[5,4,4,3,2,1,1]
 => ?
 => ? = 2
[6,5,5,4,1,1,1]
 => [7,4,4,4,3,1]
 => ? = 1
[6,5,4,3,1,1,1]
 => [7,4,4,3,2,1]
 => ? = 2
[7,6,5,2,1,1,1]
 => [7,4,3,3,3,2,1]
 => ? = 4
[5,5,5,2,1,1,1]
 => [7,4,3,3,3]
 => ? = 3
[7,5,4,2,1,1,1]
 => ?
 => ? = 3
[6,5,4,2,1,1,1]
 => [7,4,3,3,2,1]
 => ? = 3
Description
The number of parts of a partition that are not congruent 1 modulo 3.
Matching statistic: St001232
Mapping
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: 46%
Values
[1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
[2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 0
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[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]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2
[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
[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
[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
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[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
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[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]
 => [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
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 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
[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
[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
[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
[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
[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
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[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
[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]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 3
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ? = 2
[3,2,1,1]
 => [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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[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
[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
[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]
 => [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
[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]
 => [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
[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
[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
[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
[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
[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
[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
[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
[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
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => ? = 1
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => ? = 2
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 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
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
 => ? = 2
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
 => ? = 0
[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
[5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => ? = 3
[5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => ? = 2
[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
[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
[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
[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.