- 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: St000814

Mapping

St000814: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1]
 => 1
[2]
 => 1
[1,1]
 => 2
[3]
 => 1
[2,1]
 => 2
[1,1,1]
 => 4
[4]
 => 1
[3,1]
 => 2
[2,2]
 => 3
[2,1,1]
 => 5
[1,1,1,1]
 => 10
[5]
 => 1
[4,1]
 => 2
[3,2]
 => 3
[3,1,1]
 => 5
[2,2,1]
 => 7
[2,1,1,1]
 => 13
[1,1,1,1,1]
 => 26
[6]
 => 1
[5,1]
 => 2
[4,2]
 => 3
[4,1,1]
 => 5
[3,3]
 => 4
[3,2,1]
 => 8
[3,1,1,1]
 => 14
[2,2,2]
 => 11
[2,2,1,1]
 => 20
[2,1,1,1,1]
 => 38
[1,1,1,1,1,1]
 => 76
[7]
 => 1
[6,1]
 => 2
[5,2]
 => 3
[5,1,1]
 => 5
[4,3]
 => 4
[4,2,1]
 => 8
[4,1,1,1]
 => 14
[3,3,1]
 => 10
[3,2,2]
 => 13
[3,2,1,1]
 => 23
[3,1,1,1,1]
 => 42
[2,2,2,1]
 => 32
[2,2,1,1,1]
 => 60
[2,1,1,1,1,1]
 => 116
[1,1,1,1,1,1,1]
 => 232
[8]
 => 1
[7,1]
 => 2
[6,2]
 => 3
[6,1,1]
 => 5
[5,3]
 => 4
[5,2,1]
 => 8

Description

The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. For example,

$e_{22} = s_{1111} + s_{211} + s_{22}$ , so the statistic on the partition

$22$ is

$3$ .

Matching statistic: St001232
(load all 2 compositions to match this statistic)

Mapping

Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 10%●distinct values known / distinct values provided: 4%

Values

[1]
 => [1,0]
 => [1,0]
 => 0 = 1 - 1
[2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
[1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1 = 2 - 1
[3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
[2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1 = 2 - 1
[1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 4 - 1
[4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 2 - 1
[2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2 = 3 - 1
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? ∊ {5,10} - 1
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? ∊ {5,10} - 1
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 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 = 2 - 1
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 3 - 1
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {5,7,13,26} - 1
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {5,7,13,26} - 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]
 => ? ∊ {5,7,13,26} - 1
[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]
 => ? ∊ {5,7,13,26} - 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 = 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 = 2 - 1
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2 = 3 - 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]
 => ? ∊ {5,8,11,14,20,38,76} - 1
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 4 - 1
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? ∊ {5,8,11,14,20,38,76} - 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]
 => ? ∊ {5,8,11,14,20,38,76} - 1
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {5,8,11,14,20,38,76} - 1
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? ∊ {5,8,11,14,20,38,76} - 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]
 => ? ∊ {5,8,11,14,20,38,76} - 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]
 => ? ∊ {5,8,11,14,20,38,76} - 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 = 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 = 2 - 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 = 3 - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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 - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 1
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 1
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {5,8,10,13,14,23,32,42,60,116,232} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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 = 3 - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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 = 4 - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 5 - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[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]
 => ? ∊ {1,2,5,8,11,14,14,17,24,30,40,43,56,73,103,136,196,382,764} - 1
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => ? ∊ {1,2,3,5,8,11,13,14,14,19,23,24,33,43,43,53,72,77,96,131,141,184,244,347,462,668,1310,2620} - 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]
 => ? ∊ {1,2,3,5,8,11,13,14,14,19,23,24,33,43,43,53,72,77,96,131,141,184,244,347,462,668,1310,2620} - 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]
 => ? ∊ {1,2,3,5,8,11,13,14,14,19,23,24,33,43,43,53,72,77,96,131,141,184,244,347,462,668,1310,2620} - 1
[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]
 => ? ∊ {1,2,3,5,8,11,13,14,14,19,23,24,33,43,43,53,72,77,96,131,141,184,244,347,462,668,1310,2620} - 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 = 4 - 1
[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]
 => ? ∊ {1,2,3,5,8,11,13,14,14,19,23,24,33,43,43,53,72,77,96,131,141,184,244,347,462,668,1310,2620} - 1
[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]
 => ? ∊ {1,2,3,5,8,11,13,14,14,19,23,24,33,43,43,53,72,77,96,131,141,184,244,347,462,668,1310,2620} - 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 = 5 - 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 = 5 - 1
[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 - 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 = 6 - 1
[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 = 7 - 1

Description

The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.