- FindStat

Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000715

Mapping

St000715: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1]
 => 3
[2]
 => 6
[1,1]
 => 3
[3]
 => 10
[2,1]
 => 8
[1,1,1]
 => 1
[4]
 => 15
[3,1]
 => 15
[2,2]
 => 6
[2,1,1]
 => 3
[1,1,1,1]
 => 0
[5]
 => 21
[4,1]
 => 24
[3,2]
 => 15
[3,1,1]
 => 6
[2,2,1]
 => 3
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 0
[6]
 => 28
[5,1]
 => 35
[4,2]
 => 27
[4,1,1]
 => 10
[3,3]
 => 10
[3,2,1]
 => 8
[3,1,1,1]
 => 0
[2,2,2]
 => 1
[2,2,1,1]
 => 0
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 0
[7]
 => 36
[6,1]
 => 48
[5,2]
 => 42
[5,1,1]
 => 15
[4,3]
 => 24
[4,2,1]
 => 15
[4,1,1,1]
 => 0
[3,3,1]
 => 6
[3,2,2]
 => 3
[3,2,1,1]
 => 0
[3,1,1,1,1]
 => 0
[2,2,2,1]
 => 0
[2,2,1,1,1]
 => 0
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 0
[8]
 => 45
[7,1]
 => 63
[6,2]
 => 60
[6,1,1]
 => 21
[5,3]
 => 42
[5,2,1]
 => 24

Description

The number of semistandard Young tableaux of given shape and entries at most 3. This is also the dimension of the corresponding irreducible representation of

$GL_3$ .

Matching statistic: St001498
(load all 3 compositions to match this statistic)

Mapping

Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 18%●distinct values known / distinct values provided: 3%

Values

[1]
 => [1,0]
 => [1,0]
 => [1,0]
 => ? = 3
[2]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? ∊ {3,6}
[1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? ∊ {3,6}
[3]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {1,8,10}
[2,1]
 => [1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {1,8,10}
[1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {1,8,10}
[4]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,3,6,15,15}
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,3,6,15,15}
[2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {0,3,6,15,15}
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,3,6,15,15}
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,3,6,15,15}
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[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]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,3,6,15,21,24}
[6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 0
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[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]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,1,8,10,10,27,28,35}
[7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [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]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 0
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 0
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[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]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,3,6,15,15,24,36,42,48}
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [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]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [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]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,3,6,15,15,21,24,42,45,60,63}
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 0
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 0
[3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0
[2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 0
[2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0
[5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[4,3,2]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 0
[4,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => 0
[3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 0
[3,3,2,1]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0
[3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 0
[3,2,2,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => 0
[2,2,2,2,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 0
[2,2,2,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => 0
[5,3,2]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[4,4,2]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 0
[4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 0
[4,3,2,1]
 => [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => 0
[4,2,2,2]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 0
[3,3,3,1]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 0
[3,3,2,2]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 0
[3,3,2,1,1]
 => [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => 0
[3,2,2,2,1]
 => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 0
[2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 0
[2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 0
[5,4,2]
 => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[5,3,3]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => 0
[4,4,3]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 0
[4,4,2,1]
 => [1,1,1,0,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => 0
[4,3,3,1]
 => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => 0
[4,3,2,2]
 => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 0
[3,3,3,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => 0
[3,3,3,1,1]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => 0
[3,3,2,2,1]
 => [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 0
[3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => 0
[2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0
[5,5,2]
 => [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[5,4,3]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => 0
[4,4,4]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 0
[4,4,3,1]
 => [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => 0
[4,4,2,2]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 0
[4,3,3,2]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => 0
[3,3,3,3]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 0
[3,3,3,2,1]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
 => 0
[3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => 0
[2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => 0

Description

The normalised height of a Nakayama algebra with magnitude 1. We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.