searching the database
Your data matches 20 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000900
(load all 16 compositions to match this statistic)
(load all 16 compositions to match this statistic)
Mp00294: Standard tableaux —peak composition⟶ Integer compositions
St000900: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000900: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => 1
[[1,2]]
=> [2] => 1
[[1],[2]]
=> [2] => 1
[[1,2,3]]
=> [3] => 1
[[1,3],[2]]
=> [3] => 1
[[1,2],[3]]
=> [2,1] => 1
[[1],[2],[3]]
=> [3] => 1
[[1,2,3,4]]
=> [4] => 1
[[1,3,4],[2]]
=> [4] => 1
[[1,2,4],[3]]
=> [2,2] => 2
[[1,2,3],[4]]
=> [3,1] => 1
[[1,3],[2,4]]
=> [3,1] => 1
[[1,2],[3,4]]
=> [2,2] => 2
[[1,4],[2],[3]]
=> [4] => 1
[[1,3],[2],[4]]
=> [3,1] => 1
[[1,2],[3],[4]]
=> [2,2] => 2
[[1],[2],[3],[4]]
=> [4] => 1
[[1,2,3,4,5]]
=> [5] => 1
[[1,3,4,5],[2]]
=> [5] => 1
[[1,2,4,5],[3]]
=> [2,3] => 1
[[1,2,3,5],[4]]
=> [3,2] => 1
[[1,2,3,4],[5]]
=> [4,1] => 1
[[1,3,5],[2,4]]
=> [3,2] => 1
[[1,2,5],[3,4]]
=> [2,3] => 1
[[1,3,4],[2,5]]
=> [4,1] => 1
[[1,2,4],[3,5]]
=> [2,2,1] => 1
[[1,2,3],[4,5]]
=> [3,2] => 1
[[1,4,5],[2],[3]]
=> [5] => 1
[[1,3,5],[2],[4]]
=> [3,2] => 1
[[1,2,5],[3],[4]]
=> [2,3] => 1
[[1,3,4],[2],[5]]
=> [4,1] => 1
[[1,2,4],[3],[5]]
=> [2,2,1] => 1
[[1,2,3],[4],[5]]
=> [3,2] => 1
[[1,4],[2,5],[3]]
=> [4,1] => 1
[[1,3],[2,5],[4]]
=> [3,2] => 1
[[1,2],[3,5],[4]]
=> [2,3] => 1
[[1,3],[2,4],[5]]
=> [3,2] => 1
[[1,2],[3,4],[5]]
=> [2,2,1] => 1
[[1,5],[2],[3],[4]]
=> [5] => 1
[[1,4],[2],[3],[5]]
=> [4,1] => 1
[[1,3],[2],[4],[5]]
=> [3,2] => 1
[[1,2],[3],[4],[5]]
=> [2,3] => 1
[[1],[2],[3],[4],[5]]
=> [5] => 1
[[1,2,3,4,5,6]]
=> [6] => 1
[[1,3,4,5,6],[2]]
=> [6] => 1
[[1,2,4,5,6],[3]]
=> [2,4] => 1
[[1,2,3,5,6],[4]]
=> [3,3] => 2
[[1,2,3,4,6],[5]]
=> [4,2] => 1
[[1,2,3,4,5],[6]]
=> [5,1] => 1
[[1,3,5,6],[2,4]]
=> [3,3] => 2
Description
The minimal number of repetitions of a part in an integer composition.
This is the smallest letter in the word obtained by applying the delta morphism.
Matching statistic: St000902
(load all 16 compositions to match this statistic)
(load all 16 compositions to match this statistic)
Mp00294: Standard tableaux —peak composition⟶ Integer compositions
St000902: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000902: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => 1
[[1,2]]
=> [2] => 1
[[1],[2]]
=> [2] => 1
[[1,2,3]]
=> [3] => 1
[[1,3],[2]]
=> [3] => 1
[[1,2],[3]]
=> [2,1] => 1
[[1],[2],[3]]
=> [3] => 1
[[1,2,3,4]]
=> [4] => 1
[[1,3,4],[2]]
=> [4] => 1
[[1,2,4],[3]]
=> [2,2] => 2
[[1,2,3],[4]]
=> [3,1] => 1
[[1,3],[2,4]]
=> [3,1] => 1
[[1,2],[3,4]]
=> [2,2] => 2
[[1,4],[2],[3]]
=> [4] => 1
[[1,3],[2],[4]]
=> [3,1] => 1
[[1,2],[3],[4]]
=> [2,2] => 2
[[1],[2],[3],[4]]
=> [4] => 1
[[1,2,3,4,5]]
=> [5] => 1
[[1,3,4,5],[2]]
=> [5] => 1
[[1,2,4,5],[3]]
=> [2,3] => 1
[[1,2,3,5],[4]]
=> [3,2] => 1
[[1,2,3,4],[5]]
=> [4,1] => 1
[[1,3,5],[2,4]]
=> [3,2] => 1
[[1,2,5],[3,4]]
=> [2,3] => 1
[[1,3,4],[2,5]]
=> [4,1] => 1
[[1,2,4],[3,5]]
=> [2,2,1] => 1
[[1,2,3],[4,5]]
=> [3,2] => 1
[[1,4,5],[2],[3]]
=> [5] => 1
[[1,3,5],[2],[4]]
=> [3,2] => 1
[[1,2,5],[3],[4]]
=> [2,3] => 1
[[1,3,4],[2],[5]]
=> [4,1] => 1
[[1,2,4],[3],[5]]
=> [2,2,1] => 1
[[1,2,3],[4],[5]]
=> [3,2] => 1
[[1,4],[2,5],[3]]
=> [4,1] => 1
[[1,3],[2,5],[4]]
=> [3,2] => 1
[[1,2],[3,5],[4]]
=> [2,3] => 1
[[1,3],[2,4],[5]]
=> [3,2] => 1
[[1,2],[3,4],[5]]
=> [2,2,1] => 1
[[1,5],[2],[3],[4]]
=> [5] => 1
[[1,4],[2],[3],[5]]
=> [4,1] => 1
[[1,3],[2],[4],[5]]
=> [3,2] => 1
[[1,2],[3],[4],[5]]
=> [2,3] => 1
[[1],[2],[3],[4],[5]]
=> [5] => 1
[[1,2,3,4,5,6]]
=> [6] => 1
[[1,3,4,5,6],[2]]
=> [6] => 1
[[1,2,4,5,6],[3]]
=> [2,4] => 1
[[1,2,3,5,6],[4]]
=> [3,3] => 2
[[1,2,3,4,6],[5]]
=> [4,2] => 1
[[1,2,3,4,5],[6]]
=> [5,1] => 1
[[1,3,5,6],[2,4]]
=> [3,3] => 2
Description
The minimal number of repetitions of an integer composition.
Matching statistic: St000627
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000627: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00094: Integer compositions —to binary word⟶ Binary words
St000627: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => 1 => 1
[[1,2]]
=> [2] => 10 => 1
[[1],[2]]
=> [2] => 10 => 1
[[1,2,3]]
=> [3] => 100 => 1
[[1,3],[2]]
=> [2,1] => 101 => 1
[[1,2],[3]]
=> [3] => 100 => 1
[[1],[2],[3]]
=> [3] => 100 => 1
[[1,2,3,4]]
=> [4] => 1000 => 1
[[1,3,4],[2]]
=> [2,2] => 1010 => 2
[[1,2,4],[3]]
=> [3,1] => 1001 => 1
[[1,2,3],[4]]
=> [4] => 1000 => 1
[[1,3],[2,4]]
=> [2,2] => 1010 => 2
[[1,2],[3,4]]
=> [3,1] => 1001 => 1
[[1,4],[2],[3]]
=> [3,1] => 1001 => 1
[[1,3],[2],[4]]
=> [2,2] => 1010 => 2
[[1,2],[3],[4]]
=> [4] => 1000 => 1
[[1],[2],[3],[4]]
=> [4] => 1000 => 1
[[1,2,3,4,5]]
=> [5] => 10000 => 1
[[1,3,4,5],[2]]
=> [2,3] => 10100 => 1
[[1,2,4,5],[3]]
=> [3,2] => 10010 => 1
[[1,2,3,5],[4]]
=> [4,1] => 10001 => 1
[[1,2,3,4],[5]]
=> [5] => 10000 => 1
[[1,3,5],[2,4]]
=> [2,2,1] => 10101 => 1
[[1,2,5],[3,4]]
=> [3,2] => 10010 => 1
[[1,3,4],[2,5]]
=> [2,3] => 10100 => 1
[[1,2,4],[3,5]]
=> [3,2] => 10010 => 1
[[1,2,3],[4,5]]
=> [4,1] => 10001 => 1
[[1,4,5],[2],[3]]
=> [3,2] => 10010 => 1
[[1,3,5],[2],[4]]
=> [2,2,1] => 10101 => 1
[[1,2,5],[3],[4]]
=> [4,1] => 10001 => 1
[[1,3,4],[2],[5]]
=> [2,3] => 10100 => 1
[[1,2,4],[3],[5]]
=> [3,2] => 10010 => 1
[[1,2,3],[4],[5]]
=> [5] => 10000 => 1
[[1,4],[2,5],[3]]
=> [3,2] => 10010 => 1
[[1,3],[2,5],[4]]
=> [2,2,1] => 10101 => 1
[[1,2],[3,5],[4]]
=> [4,1] => 10001 => 1
[[1,3],[2,4],[5]]
=> [2,3] => 10100 => 1
[[1,2],[3,4],[5]]
=> [3,2] => 10010 => 1
[[1,5],[2],[3],[4]]
=> [4,1] => 10001 => 1
[[1,4],[2],[3],[5]]
=> [3,2] => 10010 => 1
[[1,3],[2],[4],[5]]
=> [2,3] => 10100 => 1
[[1,2],[3],[4],[5]]
=> [5] => 10000 => 1
[[1],[2],[3],[4],[5]]
=> [5] => 10000 => 1
[[1,2,3,4,5,6]]
=> [6] => 100000 => 1
[[1,3,4,5,6],[2]]
=> [2,4] => 101000 => 1
[[1,2,4,5,6],[3]]
=> [3,3] => 100100 => 2
[[1,2,3,5,6],[4]]
=> [4,2] => 100010 => 1
[[1,2,3,4,6],[5]]
=> [5,1] => 100001 => 1
[[1,2,3,4,5],[6]]
=> [6] => 100000 => 1
[[1,3,5,6],[2,4]]
=> [2,2,2] => 101010 => 3
Description
The exponent of a binary word.
This is the largest number $e$ such that $w$ is the concatenation of $e$ identical factors. This statistic is also called '''frequency'''.
Matching statistic: St000657
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St000657: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St000657: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => [1] => 1
[[1,2]]
=> [2] => [1] => 1
[[1],[2]]
=> [2] => [1] => 1
[[1,2,3]]
=> [3] => [1] => 1
[[1,3],[2]]
=> [2,1] => [1,1] => 1
[[1,2],[3]]
=> [3] => [1] => 1
[[1],[2],[3]]
=> [3] => [1] => 1
[[1,2,3,4]]
=> [4] => [1] => 1
[[1,3,4],[2]]
=> [2,2] => [2] => 2
[[1,2,4],[3]]
=> [3,1] => [1,1] => 1
[[1,2,3],[4]]
=> [4] => [1] => 1
[[1,3],[2,4]]
=> [2,2] => [2] => 2
[[1,2],[3,4]]
=> [3,1] => [1,1] => 1
[[1,4],[2],[3]]
=> [3,1] => [1,1] => 1
[[1,3],[2],[4]]
=> [2,2] => [2] => 2
[[1,2],[3],[4]]
=> [4] => [1] => 1
[[1],[2],[3],[4]]
=> [4] => [1] => 1
[[1,2,3,4,5]]
=> [5] => [1] => 1
[[1,3,4,5],[2]]
=> [2,3] => [1,1] => 1
[[1,2,4,5],[3]]
=> [3,2] => [1,1] => 1
[[1,2,3,5],[4]]
=> [4,1] => [1,1] => 1
[[1,2,3,4],[5]]
=> [5] => [1] => 1
[[1,3,5],[2,4]]
=> [2,2,1] => [2,1] => 1
[[1,2,5],[3,4]]
=> [3,2] => [1,1] => 1
[[1,3,4],[2,5]]
=> [2,3] => [1,1] => 1
[[1,2,4],[3,5]]
=> [3,2] => [1,1] => 1
[[1,2,3],[4,5]]
=> [4,1] => [1,1] => 1
[[1,4,5],[2],[3]]
=> [3,2] => [1,1] => 1
[[1,3,5],[2],[4]]
=> [2,2,1] => [2,1] => 1
[[1,2,5],[3],[4]]
=> [4,1] => [1,1] => 1
[[1,3,4],[2],[5]]
=> [2,3] => [1,1] => 1
[[1,2,4],[3],[5]]
=> [3,2] => [1,1] => 1
[[1,2,3],[4],[5]]
=> [5] => [1] => 1
[[1,4],[2,5],[3]]
=> [3,2] => [1,1] => 1
[[1,3],[2,5],[4]]
=> [2,2,1] => [2,1] => 1
[[1,2],[3,5],[4]]
=> [4,1] => [1,1] => 1
[[1,3],[2,4],[5]]
=> [2,3] => [1,1] => 1
[[1,2],[3,4],[5]]
=> [3,2] => [1,1] => 1
[[1,5],[2],[3],[4]]
=> [4,1] => [1,1] => 1
[[1,4],[2],[3],[5]]
=> [3,2] => [1,1] => 1
[[1,3],[2],[4],[5]]
=> [2,3] => [1,1] => 1
[[1,2],[3],[4],[5]]
=> [5] => [1] => 1
[[1],[2],[3],[4],[5]]
=> [5] => [1] => 1
[[1,2,3,4,5,6]]
=> [6] => [1] => 1
[[1,3,4,5,6],[2]]
=> [2,4] => [1,1] => 1
[[1,2,4,5,6],[3]]
=> [3,3] => [2] => 2
[[1,2,3,5,6],[4]]
=> [4,2] => [1,1] => 1
[[1,2,3,4,6],[5]]
=> [5,1] => [1,1] => 1
[[1,2,3,4,5],[6]]
=> [6] => [1] => 1
[[1,3,5,6],[2,4]]
=> [2,2,2] => [3] => 3
Description
The smallest part of an integer composition.
Matching statistic: St000667
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000667: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000667: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => [1]
=> [1]
=> 1
[[1,2]]
=> [2] => [2]
=> [1,1]
=> 1
[[1],[2]]
=> [2] => [2]
=> [1,1]
=> 1
[[1,2,3]]
=> [3] => [3]
=> [1,1,1]
=> 1
[[1,3],[2]]
=> [2,1] => [2,1]
=> [2,1]
=> 1
[[1,2],[3]]
=> [3] => [3]
=> [1,1,1]
=> 1
[[1],[2],[3]]
=> [3] => [3]
=> [1,1,1]
=> 1
[[1,2,3,4]]
=> [4] => [4]
=> [1,1,1,1]
=> 1
[[1,3,4],[2]]
=> [2,2] => [2,2]
=> [2,2]
=> 2
[[1,2,4],[3]]
=> [3,1] => [3,1]
=> [2,1,1]
=> 1
[[1,2,3],[4]]
=> [4] => [4]
=> [1,1,1,1]
=> 1
[[1,3],[2,4]]
=> [2,2] => [2,2]
=> [2,2]
=> 2
[[1,2],[3,4]]
=> [3,1] => [3,1]
=> [2,1,1]
=> 1
[[1,4],[2],[3]]
=> [3,1] => [3,1]
=> [2,1,1]
=> 1
[[1,3],[2],[4]]
=> [2,2] => [2,2]
=> [2,2]
=> 2
[[1,2],[3],[4]]
=> [4] => [4]
=> [1,1,1,1]
=> 1
[[1],[2],[3],[4]]
=> [4] => [4]
=> [1,1,1,1]
=> 1
[[1,2,3,4,5]]
=> [5] => [5]
=> [1,1,1,1,1]
=> 1
[[1,3,4,5],[2]]
=> [2,3] => [3,2]
=> [2,2,1]
=> 1
[[1,2,4,5],[3]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,2,3,5],[4]]
=> [4,1] => [4,1]
=> [2,1,1,1]
=> 1
[[1,2,3,4],[5]]
=> [5] => [5]
=> [1,1,1,1,1]
=> 1
[[1,3,5],[2,4]]
=> [2,2,1] => [2,2,1]
=> [3,2]
=> 1
[[1,2,5],[3,4]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,3,4],[2,5]]
=> [2,3] => [3,2]
=> [2,2,1]
=> 1
[[1,2,4],[3,5]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,2,3],[4,5]]
=> [4,1] => [4,1]
=> [2,1,1,1]
=> 1
[[1,4,5],[2],[3]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,3,5],[2],[4]]
=> [2,2,1] => [2,2,1]
=> [3,2]
=> 1
[[1,2,5],[3],[4]]
=> [4,1] => [4,1]
=> [2,1,1,1]
=> 1
[[1,3,4],[2],[5]]
=> [2,3] => [3,2]
=> [2,2,1]
=> 1
[[1,2,4],[3],[5]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,2,3],[4],[5]]
=> [5] => [5]
=> [1,1,1,1,1]
=> 1
[[1,4],[2,5],[3]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,3],[2,5],[4]]
=> [2,2,1] => [2,2,1]
=> [3,2]
=> 1
[[1,2],[3,5],[4]]
=> [4,1] => [4,1]
=> [2,1,1,1]
=> 1
[[1,3],[2,4],[5]]
=> [2,3] => [3,2]
=> [2,2,1]
=> 1
[[1,2],[3,4],[5]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,5],[2],[3],[4]]
=> [4,1] => [4,1]
=> [2,1,1,1]
=> 1
[[1,4],[2],[3],[5]]
=> [3,2] => [3,2]
=> [2,2,1]
=> 1
[[1,3],[2],[4],[5]]
=> [2,3] => [3,2]
=> [2,2,1]
=> 1
[[1,2],[3],[4],[5]]
=> [5] => [5]
=> [1,1,1,1,1]
=> 1
[[1],[2],[3],[4],[5]]
=> [5] => [5]
=> [1,1,1,1,1]
=> 1
[[1,2,3,4,5,6]]
=> [6] => [6]
=> [1,1,1,1,1,1]
=> 1
[[1,3,4,5,6],[2]]
=> [2,4] => [4,2]
=> [2,2,1,1]
=> 1
[[1,2,4,5,6],[3]]
=> [3,3] => [3,3]
=> [2,2,2]
=> 2
[[1,2,3,5,6],[4]]
=> [4,2] => [4,2]
=> [2,2,1,1]
=> 1
[[1,2,3,4,6],[5]]
=> [5,1] => [5,1]
=> [2,1,1,1,1]
=> 1
[[1,2,3,4,5],[6]]
=> [6] => [6]
=> [1,1,1,1,1,1]
=> 1
[[1,3,5,6],[2,4]]
=> [2,2,2] => [2,2,2]
=> [3,3]
=> 3
Description
The greatest common divisor of the parts of the partition.
Matching statistic: St000775
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000775: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000775: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => [1] => ([],1)
=> 1
[[1,2]]
=> [2] => [1] => ([],1)
=> 1
[[1],[2]]
=> [2] => [1] => ([],1)
=> 1
[[1,2,3]]
=> [3] => [1] => ([],1)
=> 1
[[1,3],[2]]
=> [2,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,2],[3]]
=> [3] => [1] => ([],1)
=> 1
[[1],[2],[3]]
=> [3] => [1] => ([],1)
=> 1
[[1,2,3,4]]
=> [4] => [1] => ([],1)
=> 1
[[1,3,4],[2]]
=> [2,2] => [2] => ([],2)
=> 2
[[1,2,4],[3]]
=> [3,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3],[4]]
=> [4] => [1] => ([],1)
=> 1
[[1,3],[2,4]]
=> [2,2] => [2] => ([],2)
=> 2
[[1,2],[3,4]]
=> [3,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,4],[2],[3]]
=> [3,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,3],[2],[4]]
=> [2,2] => [2] => ([],2)
=> 2
[[1,2],[3],[4]]
=> [4] => [1] => ([],1)
=> 1
[[1],[2],[3],[4]]
=> [4] => [1] => ([],1)
=> 1
[[1,2,3,4,5]]
=> [5] => [1] => ([],1)
=> 1
[[1,3,4,5],[2]]
=> [2,3] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,4,5],[3]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3,5],[4]]
=> [4,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3,4],[5]]
=> [5] => [1] => ([],1)
=> 1
[[1,3,5],[2,4]]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[[1,2,5],[3,4]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,3,4],[2,5]]
=> [2,3] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,4],[3,5]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3],[4,5]]
=> [4,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,4,5],[2],[3]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,3,5],[2],[4]]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[[1,2,5],[3],[4]]
=> [4,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,3,4],[2],[5]]
=> [2,3] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,4],[3],[5]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3],[4],[5]]
=> [5] => [1] => ([],1)
=> 1
[[1,4],[2,5],[3]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,3],[2,5],[4]]
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[[1,2],[3,5],[4]]
=> [4,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,3],[2,4],[5]]
=> [2,3] => [1,1] => ([(0,1)],2)
=> 1
[[1,2],[3,4],[5]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,5],[2],[3],[4]]
=> [4,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,4],[2],[3],[5]]
=> [3,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,3],[2],[4],[5]]
=> [2,3] => [1,1] => ([(0,1)],2)
=> 1
[[1,2],[3],[4],[5]]
=> [5] => [1] => ([],1)
=> 1
[[1],[2],[3],[4],[5]]
=> [5] => [1] => ([],1)
=> 1
[[1,2,3,4,5,6]]
=> [6] => [1] => ([],1)
=> 1
[[1,3,4,5,6],[2]]
=> [2,4] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,4,5,6],[3]]
=> [3,3] => [2] => ([],2)
=> 2
[[1,2,3,5,6],[4]]
=> [4,2] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3,4,6],[5]]
=> [5,1] => [1,1] => ([(0,1)],2)
=> 1
[[1,2,3,4,5],[6]]
=> [6] => [1] => ([],1)
=> 1
[[1,3,5,6],[2,4]]
=> [2,2,2] => [3] => ([],3)
=> 3
Description
The multiplicity of the largest eigenvalue in a graph.
Matching statistic: St001236
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
St001236: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
St001236: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => [1] => [1] => 1
[[1,2]]
=> [2] => [1] => [1] => 1
[[1],[2]]
=> [2] => [1] => [1] => 1
[[1,2,3]]
=> [3] => [1] => [1] => 1
[[1,3],[2]]
=> [2,1] => [1,1] => [2] => 1
[[1,2],[3]]
=> [3] => [1] => [1] => 1
[[1],[2],[3]]
=> [3] => [1] => [1] => 1
[[1,2,3,4]]
=> [4] => [1] => [1] => 1
[[1,3,4],[2]]
=> [2,2] => [2] => [1,1] => 2
[[1,2,4],[3]]
=> [3,1] => [1,1] => [2] => 1
[[1,2,3],[4]]
=> [4] => [1] => [1] => 1
[[1,3],[2,4]]
=> [2,2] => [2] => [1,1] => 2
[[1,2],[3,4]]
=> [3,1] => [1,1] => [2] => 1
[[1,4],[2],[3]]
=> [3,1] => [1,1] => [2] => 1
[[1,3],[2],[4]]
=> [2,2] => [2] => [1,1] => 2
[[1,2],[3],[4]]
=> [4] => [1] => [1] => 1
[[1],[2],[3],[4]]
=> [4] => [1] => [1] => 1
[[1,2,3,4,5]]
=> [5] => [1] => [1] => 1
[[1,3,4,5],[2]]
=> [2,3] => [1,1] => [2] => 1
[[1,2,4,5],[3]]
=> [3,2] => [1,1] => [2] => 1
[[1,2,3,5],[4]]
=> [4,1] => [1,1] => [2] => 1
[[1,2,3,4],[5]]
=> [5] => [1] => [1] => 1
[[1,3,5],[2,4]]
=> [2,2,1] => [2,1] => [2,1] => 1
[[1,2,5],[3,4]]
=> [3,2] => [1,1] => [2] => 1
[[1,3,4],[2,5]]
=> [2,3] => [1,1] => [2] => 1
[[1,2,4],[3,5]]
=> [3,2] => [1,1] => [2] => 1
[[1,2,3],[4,5]]
=> [4,1] => [1,1] => [2] => 1
[[1,4,5],[2],[3]]
=> [3,2] => [1,1] => [2] => 1
[[1,3,5],[2],[4]]
=> [2,2,1] => [2,1] => [2,1] => 1
[[1,2,5],[3],[4]]
=> [4,1] => [1,1] => [2] => 1
[[1,3,4],[2],[5]]
=> [2,3] => [1,1] => [2] => 1
[[1,2,4],[3],[5]]
=> [3,2] => [1,1] => [2] => 1
[[1,2,3],[4],[5]]
=> [5] => [1] => [1] => 1
[[1,4],[2,5],[3]]
=> [3,2] => [1,1] => [2] => 1
[[1,3],[2,5],[4]]
=> [2,2,1] => [2,1] => [2,1] => 1
[[1,2],[3,5],[4]]
=> [4,1] => [1,1] => [2] => 1
[[1,3],[2,4],[5]]
=> [2,3] => [1,1] => [2] => 1
[[1,2],[3,4],[5]]
=> [3,2] => [1,1] => [2] => 1
[[1,5],[2],[3],[4]]
=> [4,1] => [1,1] => [2] => 1
[[1,4],[2],[3],[5]]
=> [3,2] => [1,1] => [2] => 1
[[1,3],[2],[4],[5]]
=> [2,3] => [1,1] => [2] => 1
[[1,2],[3],[4],[5]]
=> [5] => [1] => [1] => 1
[[1],[2],[3],[4],[5]]
=> [5] => [1] => [1] => 1
[[1,2,3,4,5,6]]
=> [6] => [1] => [1] => 1
[[1,3,4,5,6],[2]]
=> [2,4] => [1,1] => [2] => 1
[[1,2,4,5,6],[3]]
=> [3,3] => [2] => [1,1] => 2
[[1,2,3,5,6],[4]]
=> [4,2] => [1,1] => [2] => 1
[[1,2,3,4,6],[5]]
=> [5,1] => [1,1] => [2] => 1
[[1,2,3,4,5],[6]]
=> [6] => [1] => [1] => 1
[[1,3,5,6],[2,4]]
=> [2,2,2] => [3] => [1,1,1] => 3
Description
The dominant dimension of the corresponding Comp-Nakayama algebra.
Matching statistic: St001199
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 25%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 25%
Values
[[1]]
=> [1] => [1] => [1,0]
=> ? = 1
[[1,2]]
=> [1,2] => [1,2] => [1,0,1,0]
=> 1
[[1],[2]]
=> [2,1] => [2,1] => [1,1,0,0]
=> ? = 1
[[1,2,3]]
=> [1,2,3] => [1,3,2] => [1,0,1,1,0,0]
=> 1
[[1,3],[2]]
=> [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 1
[[1,2],[3]]
=> [3,1,2] => [3,1,2] => [1,1,1,0,0,0]
=> ? ∊ {1,1}
[[1],[2],[3]]
=> [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? ∊ {1,1}
[[1,2,3,4]]
=> [1,2,3,4] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1
[[1,3,4],[2]]
=> [2,1,3,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 1
[[1,2,4],[3]]
=> [3,1,2,4] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 1
[[1,2,3],[4]]
=> [4,1,2,3] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,2,2,2}
[[1,3],[2,4]]
=> [2,4,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 1
[[1,2],[3,4]]
=> [3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 1
[[1,4],[2],[3]]
=> [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 1
[[1,3],[2],[4]]
=> [4,2,1,3] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,2,2,2}
[[1,2],[3],[4]]
=> [4,3,1,2] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,2,2,2}
[[1],[2],[3],[4]]
=> [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,2,2,2}
[[1,2,3,4,5]]
=> [1,2,3,4,5] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1
[[1,3,4,5],[2]]
=> [2,1,3,4,5] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1
[[1,2,4,5],[3]]
=> [3,1,2,4,5] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 1
[[1,2,3,5],[4]]
=> [4,1,2,3,5] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[[1,2,3,4],[5]]
=> [5,1,2,3,4] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,3,5],[2,4]]
=> [2,4,1,3,5] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1
[[1,2,5],[3,4]]
=> [3,4,1,2,5] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[[1,3,4],[2,5]]
=> [2,5,1,3,4] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1
[[1,2,4],[3,5]]
=> [3,5,1,2,4] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[[1,2,3],[4,5]]
=> [4,5,1,2,3] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1
[[1,4,5],[2],[3]]
=> [3,2,1,4,5] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 1
[[1,3,5],[2],[4]]
=> [4,2,1,3,5] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 1
[[1,2,5],[3],[4]]
=> [4,3,1,2,5] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 1
[[1,3,4],[2],[5]]
=> [5,2,1,3,4] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2,4],[3],[5]]
=> [5,3,1,2,4] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2,3],[4],[5]]
=> [5,4,1,2,3] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,4],[2,5],[3]]
=> [3,2,5,1,4] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0]
=> 1
[[1,3],[2,5],[4]]
=> [4,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[[1,2],[3,5],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[[1,3],[2,4],[5]]
=> [5,2,4,1,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2],[3,4],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[[1,4],[2],[3],[5]]
=> [5,3,2,1,4] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,3],[2],[4],[5]]
=> [5,4,2,1,3] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 1
[[1,3,4,5,6],[2]]
=> [2,1,3,4,5,6] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0]
=> 1
[[1,2,4,5,6],[3]]
=> [3,1,2,4,5,6] => [3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0]
=> 1
[[1,2,3,5,6],[4]]
=> [4,1,2,3,5,6] => [4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1
[[1,2,3,4,6],[5]]
=> [5,1,2,3,4,6] => [5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5,6],[2,4]]
=> [2,4,1,3,5,6] => [2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> 1
[[1,2,5,6],[3,4]]
=> [3,4,1,2,5,6] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[[1,3,4,6],[2,5]]
=> [2,5,1,3,4,6] => [2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> 1
[[1,2,4,6],[3,5]]
=> [3,5,1,2,4,6] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[[1,2,3,6],[4,5]]
=> [4,5,1,2,3,6] => [4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1
[[1,3,4,5],[2,6]]
=> [2,6,1,3,4,5] => [2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> 1
[[1,2,4,5],[3,6]]
=> [3,6,1,2,4,5] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[[1,2,3,5],[4,6]]
=> [4,6,1,2,3,5] => [4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1
[[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => [5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1
[[1,4,5,6],[2],[3]]
=> [3,2,1,4,5,6] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> 1
[[1,3,5,6],[2],[4]]
=> [4,2,1,3,5,6] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0]
=> 1
[[1,2,5,6],[3],[4]]
=> [4,3,1,2,5,6] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0]
=> 1
[[1,3,4,6],[2],[5]]
=> [5,2,1,3,4,6] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1
[[1,2,4,6],[3],[5]]
=> [5,3,1,2,4,6] => [5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1
[[1,2,3,6],[4],[5]]
=> [5,4,1,2,3,6] => [5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1
[[1,3,4,5],[2],[6]]
=> [6,2,1,3,4,5] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4,5],[3],[6]]
=> [6,3,1,2,4,5] => [6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,5],[4],[6]]
=> [6,4,1,2,3,5] => [6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2,4,6]]
=> [2,4,6,1,3,5] => [2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> 1
[[1,2,5],[3,4,6]]
=> [3,4,6,1,2,5] => [3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[[1,3,4],[2,5,6]]
=> [2,5,6,1,3,4] => [2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> 1
[[1,2,4],[3,5,6]]
=> [3,5,6,1,2,4] => [3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1
[[1,3,5],[2,4],[6]]
=> [6,2,4,1,3,5] => [6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,5],[3,4],[6]]
=> [6,3,4,1,2,5] => [6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4],[2,5],[6]]
=> [6,2,5,1,3,4] => [6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4],[3,5],[6]]
=> [6,3,5,1,2,4] => [6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => [6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,5],[2],[3],[6]]
=> [6,3,2,1,4,5] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2],[4],[6]]
=> [6,4,2,1,3,5] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,5],[3],[4],[6]]
=> [6,4,3,1,2,5] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4],[2],[5],[6]]
=> [6,5,2,1,3,4] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4],[3],[5],[6]]
=> [6,5,3,1,2,4] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4],[2,5],[3],[6]]
=> [6,3,2,5,1,4] => [6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3],[2,5],[4],[6]]
=> [6,4,2,5,1,3] => [6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3,5],[4],[6]]
=> [6,4,3,5,1,2] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3],[2,4],[5],[6]]
=> [6,5,2,4,1,3] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3,4],[5],[6]]
=> [6,5,3,4,1,2] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,5],[2],[3],[4],[6]]
=> [6,4,3,2,1,5] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4],[2],[3],[5],[6]]
=> [6,5,3,2,1,4] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3],[2],[4],[5],[6]]
=> [6,5,4,2,1,3] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,4,5,6],[7]]
=> [7,1,2,3,4,5,6] => [7,1,6,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,3,4,5,6],[2],[7]]
=> [7,2,1,3,4,5,6] => [7,2,1,6,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,4,5,6],[3],[7]]
=> [7,3,1,2,4,5,6] => [7,3,1,6,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,3,5,6],[4],[7]]
=> [7,4,1,2,3,5,6] => [7,4,1,6,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4,6],[5],[7]]
=> [7,5,1,2,3,4,6] => [7,5,1,6,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4,5],[6],[7]]
=> [7,6,1,2,3,4,5] => [7,6,1,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001820
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001820: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001820: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Values
[[1]]
=> [1] => [1] => ([(0,1)],2)
=> 1
[[1,2]]
=> [1,2] => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[1],[2]]
=> [2,1] => [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[[1,2,3]]
=> [1,2,3] => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
[[1,3],[2]]
=> [2,1,3] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
[[1,2],[3]]
=> [3,1,2] => [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
[[1],[2],[3]]
=> [3,2,1] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
[[1,2,3,4]]
=> [1,2,3,4] => [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 2
[[1,3,4],[2]]
=> [2,1,3,4] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1
[[1,2,4],[3]]
=> [3,1,2,4] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
[[1,2,3],[4]]
=> [4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> 1
[[1,3],[2,4]]
=> [2,4,1,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1
[[1,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 2
[[1,4],[2],[3]]
=> [3,2,1,4] => [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> 1
[[1,3],[2],[4]]
=> [4,2,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
[[1,2],[3],[4]]
=> [4,3,1,2] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 1
[[1],[2],[3],[4]]
=> [4,3,2,1] => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 2
[[1,2,3,4,5]]
=> [1,2,3,4,5] => [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,3,4,5],[2]]
=> [2,1,3,4,5] => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,4,5],[3]]
=> [3,1,2,4,5] => [3,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,2,3,5],[4]]
=> [4,1,2,3,5] => [3,4,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,2,3,4],[5]]
=> [5,1,2,3,4] => [3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,3,5],[2,4]]
=> [2,4,1,3,5] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 1
[[1,2,5],[3,4]]
=> [3,4,1,2,5] => [4,1,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,3,4],[2,5]]
=> [2,5,1,3,4] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,4],[3,5]]
=> [3,5,1,2,4] => [4,1,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,2,3],[4,5]]
=> [4,5,1,2,3] => [4,5,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,4,5],[2],[3]]
=> [3,2,1,4,5] => [2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,3,5],[2],[4]]
=> [4,2,1,3,5] => [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1
[[1,2,5],[3],[4]]
=> [4,3,1,2,5] => [4,2,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,3,4],[2],[5]]
=> [5,2,1,3,4] => [2,4,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,2,4],[3],[5]]
=> [5,3,1,2,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1
[[1,2,3],[4],[5]]
=> [5,4,1,2,3] => [4,5,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,4],[2,5],[3]]
=> [3,2,5,1,4] => [2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,3],[2,5],[4]]
=> [4,2,5,1,3] => [2,5,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,2],[3,5],[4]]
=> [4,3,5,1,2] => [5,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,3],[2,4],[5]]
=> [5,2,4,1,3] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1
[[1,2],[3,4],[5]]
=> [5,3,4,1,2] => [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => [3,2,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,4],[2],[3],[5]]
=> [5,3,2,1,4] => [3,2,5,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,3],[2],[4],[5]]
=> [5,4,2,1,3] => [3,5,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 1
[[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => [5,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => [4,3,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => [2,3,4,5,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,13),(3,7),(4,13),(4,16),(5,14),(5,17),(6,16),(6,17),(8,12),(9,12),(10,8),(11,9),(12,7),(13,10),(14,11),(15,8),(15,9),(16,10),(16,15),(17,11),(17,15)],18)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,5,6],[2]]
=> [2,1,3,4,5,6] => [1,3,4,5,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,13),(3,12),(4,7),(5,12),(5,14),(6,13),(6,14),(8,11),(9,8),(10,8),(11,7),(12,9),(13,10),(14,9),(14,10)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4,5,6],[3]]
=> [3,1,2,4,5,6] => [3,1,4,5,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,5,6],[4]]
=> [4,1,2,3,5,6] => [3,4,1,5,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,4,6],[5]]
=> [5,1,2,3,4,6] => [3,4,5,1,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => [3,4,5,6,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,13),(3,12),(4,11),(5,11),(5,14),(6,12),(6,14),(8,10),(9,10),(10,7),(11,8),(12,9),(13,7),(14,8),(14,9)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5,6],[2,4]]
=> [2,4,1,3,5,6] => [1,4,2,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,5,6],[3,4]]
=> [3,4,1,2,5,6] => [4,1,2,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,6],[2,5]]
=> [2,5,1,3,4,6] => [1,4,5,2,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4,6],[3,5]]
=> [3,5,1,2,4,6] => [4,1,5,2,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,3,6],[4,5]]
=> [4,5,1,2,3,6] => [4,5,1,2,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,5],[2,6]]
=> [2,6,1,3,4,5] => [1,4,5,6,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,7),(5,7),(6,8),(6,9),(7,12),(8,11),(9,11),(11,12),(12,10)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4,5],[3,6]]
=> [3,6,1,2,4,5] => [4,1,5,6,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,5],[4,6]]
=> [4,6,1,2,3,5] => [4,5,1,6,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => [4,5,6,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,13),(6,10),(6,11),(8,7),(9,7),(10,8),(11,8),(12,9),(13,9)],14)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,5,6],[2],[3]]
=> [3,2,1,4,5,6] => [2,1,4,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,7),(5,7),(6,8),(6,9),(7,12),(8,11),(9,11),(10,12),(11,10)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5,6],[2],[4]]
=> [4,2,1,3,5,6] => [2,4,1,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,5,6],[3],[4]]
=> [4,3,1,2,5,6] => [4,2,1,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,6],[2],[5]]
=> [5,2,1,3,4,6] => [2,4,5,1,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,4,6],[3],[5]]
=> [5,3,1,2,4,6] => [4,2,5,1,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,3,6],[4],[5]]
=> [5,4,1,2,3,6] => [4,5,2,1,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,5],[2],[6]]
=> [6,2,1,3,4,5] => [2,4,5,6,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4,5],[3],[6]]
=> [6,3,1,2,4,5] => [4,2,5,6,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,3,5],[4],[6]]
=> [6,4,1,2,3,5] => [4,5,2,6,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => [4,5,6,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,8),(3,7),(4,9),(5,9),(6,7),(6,8),(7,11),(8,11),(9,10),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2,4,6]]
=> [2,4,6,1,3,5] => [1,5,2,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,5],[3,4,6]]
=> [3,4,6,1,2,5] => [5,1,2,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4],[2,5,6]]
=> [2,5,6,1,3,4] => [1,5,6,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,7),(5,7),(6,8),(6,9),(7,12),(8,11),(9,11),(11,12),(12,10)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4],[3,5,6]]
=> [3,5,6,1,2,4] => [5,1,6,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,13),(3,12),(4,11),(5,11),(5,14),(6,12),(6,14),(8,10),(9,10),(10,7),(11,8),(12,9),(13,7),(14,8),(14,9)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,6],[2,5],[3]]
=> [3,2,5,1,4,6] => [2,1,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(9,8)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,6],[2,5],[4]]
=> [4,2,5,1,3,6] => [2,5,1,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,6],[3,5],[4]]
=> [4,3,5,1,2,6] => [5,2,1,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,6],[2,4],[5]]
=> [5,2,4,1,3,6] => [2,5,3,1,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,6],[3,4],[5]]
=> [5,3,4,1,2,6] => [5,2,3,1,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,5],[2,6],[3]]
=> [3,2,6,1,4,5] => [2,1,5,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,10),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2,6],[4]]
=> [4,2,6,1,3,5] => [2,5,1,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,5],[3,6],[4]]
=> [4,3,6,1,2,5] => [5,2,1,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4],[2,6],[5]]
=> [5,2,6,1,3,4] => [2,5,6,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4],[3,6],[5]]
=> [5,3,6,1,2,4] => [5,2,6,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,3],[4,6],[5]]
=> [5,4,6,1,2,3] => [5,6,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,9),(5,9),(6,7),(6,10),(7,12),(8,11),(9,10),(10,12),(12,11)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2,4],[6]]
=> [6,2,4,1,3,5] => [2,5,3,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,5],[3,4],[6]]
=> [6,3,4,1,2,5] => [5,2,3,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,3,4],[2,5],[6]]
=> [6,2,5,1,3,4] => [2,5,6,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,4],[3,5],[6]]
=> [6,3,5,1,2,4] => [5,2,6,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => [5,6,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,11),(8,9),(9,10),(10,11)],12)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => [3,2,1,5,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,8),(3,7),(4,9),(5,9),(6,7),(6,8),(7,11),(8,11),(9,10),(10,12),(11,12)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,6],[2],[3],[5]]
=> [5,3,2,1,4,6] => [3,2,5,1,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,3,6],[2],[4],[5]]
=> [5,4,2,1,3,6] => [3,5,2,1,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,6],[3],[4],[5]]
=> [5,4,3,1,2,6] => [5,3,2,1,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,5],[2],[3],[6]]
=> [6,3,2,1,4,5] => [3,2,5,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2],[4],[6]]
=> [6,4,2,1,3,5] => [3,5,2,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
[[1,2,5],[3],[4],[6]]
=> [6,4,3,1,2,5] => [5,3,2,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,3,4],[2],[5],[6]]
=> [6,5,2,1,3,4] => [3,5,6,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4],[3],[5],[6]]
=> [6,5,3,1,2,4] => [5,3,6,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 1
[[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => [5,6,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,7),(5,7),(6,8),(6,9),(7,12),(8,11),(9,11),(10,12),(11,10)],13)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4],[2,5],[3,6]]
=> [3,6,2,5,1,4] => [3,1,6,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 1
Description
The size of the image of the pop stack sorting operator.
The pop stack sorting operator is defined by $Pop_L^\downarrow(x) = x\wedge\bigwedge\{y\in L\mid y\lessdot x\}$. This statistic returns the size of $Pop_L^\downarrow(L)\}$.
Matching statistic: St001632
Mp00106: Standard tableaux —catabolism⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 25%
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 25%
Values
[[1]]
=> [[1]]
=> [1] => ([],1)
=> ? = 1
[[1,2]]
=> [[1,2]]
=> [1,2] => ([(0,1)],2)
=> 1
[[1],[2]]
=> [[1,2]]
=> [1,2] => ([(0,1)],2)
=> 1
[[1,2,3]]
=> [[1,2,3]]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[[1,3],[2]]
=> [[1,2],[3]]
=> [3,1,2] => ([(1,2)],3)
=> ? ∊ {1,1}
[[1,2],[3]]
=> [[1,2,3]]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[[1],[2],[3]]
=> [[1,2],[3]]
=> [3,1,2] => ([(1,2)],3)
=> ? ∊ {1,1}
[[1,2,3,4]]
=> [[1,2,3,4]]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[[1,3,4],[2]]
=> [[1,2,4],[3]]
=> [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[1,2,4],[3]]
=> [[1,2,3],[4]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {1,2,2,2}
[[1,2,3],[4]]
=> [[1,2,3,4]]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[[1,3],[2,4]]
=> [[1,2,4],[3]]
=> [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[1,2],[3,4]]
=> [[1,2,3,4]]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[[1,4],[2],[3]]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {1,2,2,2}
[[1,3],[2],[4]]
=> [[1,2,4],[3]]
=> [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[1,2],[3],[4]]
=> [[1,2,3],[4]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {1,2,2,2}
[[1],[2],[3],[4]]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {1,2,2,2}
[[1,2,3,4,5]]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[1,3,4,5],[2]]
=> [[1,2,4,5],[3]]
=> [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 1
[[1,2,4,5],[3]]
=> [[1,2,3,5],[4]]
=> [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 1
[[1,2,3,5],[4]]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4],[5]]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[1,3,5],[2,4]]
=> [[1,2,4],[3,5]]
=> [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> 1
[[1,2,5],[3,4]]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,3,4],[2,5]]
=> [[1,2,4,5],[3]]
=> [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 1
[[1,2,4],[3,5]]
=> [[1,2,3,5],[4]]
=> [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 1
[[1,2,3],[4,5]]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[[1,4,5],[2],[3]]
=> [[1,2,5],[3],[4]]
=> [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
[[1,3,5],[2],[4]]
=> [[1,2,4],[3],[5]]
=> [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2,5],[3],[4]]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,3,4],[2],[5]]
=> [[1,2,4,5],[3]]
=> [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 1
[[1,2,4],[3],[5]]
=> [[1,2,3,5],[4]]
=> [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 1
[[1,2,3],[4],[5]]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,4],[2,5],[3]]
=> [[1,2,5],[3],[4]]
=> [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
[[1,3],[2,5],[4]]
=> [[1,2,4,5],[3]]
=> [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 1
[[1,2],[3,5],[4]]
=> [[1,2,3,5],[4]]
=> [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 1
[[1,3],[2,4],[5]]
=> [[1,2,4],[3,5]]
=> [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> 1
[[1,2],[3,4],[5]]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,5],[2],[3],[4]]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,4],[2],[3],[5]]
=> [[1,2,5],[3],[4]]
=> [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
[[1,3],[2],[4],[5]]
=> [[1,2,4],[3],[5]]
=> [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2],[3],[4],[5]]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1],[2],[3],[4],[5]]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4,5,6]]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[[1,3,4,5,6],[2]]
=> [[1,2,4,5,6],[3]]
=> [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> 1
[[1,2,4,5,6],[3]]
=> [[1,2,3,5,6],[4]]
=> [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> 1
[[1,2,3,5,6],[4]]
=> [[1,2,3,4,6],[5]]
=> [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> 1
[[1,2,3,4,6],[5]]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,4,5],[6]]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[[1,3,5,6],[2,4]]
=> [[1,2,4,6],[3,5]]
=> [3,5,1,2,4,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> 1
[[1,2,5,6],[3,4]]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,6],[2,5]]
=> [[1,2,4,5],[3,6]]
=> [3,6,1,2,4,5] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> 1
[[1,2,4,6],[3,5]]
=> [[1,2,3,5],[4,6]]
=> [4,6,1,2,3,5] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
=> 1
[[1,2,3,6],[4,5]]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,5],[2,6]]
=> [[1,2,4,5,6],[3]]
=> [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> 1
[[1,2,4,5],[3,6]]
=> [[1,2,3,5,6],[4]]
=> [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> 1
[[1,2,3,5],[4,6]]
=> [[1,2,3,4,6],[5]]
=> [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> 1
[[1,2,3,4],[5,6]]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[[1,4,5,6],[2],[3]]
=> [[1,2,5,6],[3],[4]]
=> [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> 1
[[1,3,5,6],[2],[4]]
=> [[1,2,4,6],[3],[5]]
=> [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> 1
[[1,2,5,6],[3],[4]]
=> [[1,2,3,6],[4],[5]]
=> [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> 1
[[1,3,4,6],[2],[5]]
=> [[1,2,4,5],[3],[6]]
=> [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4,6],[3],[5]]
=> [[1,2,3,5],[4],[6]]
=> [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3,6],[4],[5]]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,5],[2],[6]]
=> [[1,2,4,5,6],[3]]
=> [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> 1
[[1,2,4,5],[3],[6]]
=> [[1,2,3,5,6],[4]]
=> [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> 1
[[1,2,3,5],[4],[6]]
=> [[1,2,3,4,6],[5]]
=> [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> 1
[[1,2,3,4],[5],[6]]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,5],[2,4,6]]
=> [[1,2,4,6],[3,5]]
=> [3,5,1,2,4,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> 1
[[1,2,5],[3,4,6]]
=> [[1,2,3,4,6],[5]]
=> [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> 1
[[1,3,4],[2,5,6]]
=> [[1,2,4,5,6],[3]]
=> [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> 1
[[1,2,4],[3,5,6]]
=> [[1,2,3,5,6],[4]]
=> [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> 1
[[1,2,3],[4,5,6]]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[[1,4,6],[2,5],[3]]
=> [[1,2,5],[3,6],[4]]
=> [4,3,6,1,2,5] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)
=> 1
[[1,3,6],[2,5],[4]]
=> [[1,2,4,5],[3],[6]]
=> [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,6],[3,5],[4]]
=> [[1,2,3,5],[4],[6]]
=> [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,6],[2,4],[5]]
=> [[1,2,4],[3,5],[6]]
=> [6,3,5,1,2,4] => ([(1,4),(2,3),(2,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,6],[3,4],[5]]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,5],[3,4],[6]]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3],[4,5],[6]]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4,6],[2],[3],[5]]
=> [[1,2,5],[3],[4],[6]]
=> [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,6],[2],[4],[5]]
=> [[1,2,4],[3],[5],[6]]
=> [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,6],[3],[4],[5]]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4],[2],[5],[6]]
=> [[1,2,4,5],[3],[6]]
=> [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,4],[3],[5],[6]]
=> [[1,2,3,5],[4],[6]]
=> [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2,3],[4],[5],[6]]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3,4],[5,6]]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3],[2,5],[4],[6]]
=> [[1,2,4,5],[3],[6]]
=> [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3,5],[4],[6]]
=> [[1,2,3,5],[4],[6]]
=> [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3],[2,4],[5],[6]]
=> [[1,2,4],[3,5],[6]]
=> [6,3,5,1,2,4] => ([(1,4),(2,3),(2,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3,4],[5],[6]]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,6],[2],[3],[4],[5]]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => ([(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,4],[2],[3],[5],[6]]
=> [[1,2,5],[3],[4],[6]]
=> [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3],[2],[4],[5],[6]]
=> [[1,2,4],[3],[5],[6]]
=> [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,2],[3],[4],[5],[6]]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1],[2],[3],[4],[5],[6]]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => ([(4,5)],6)
=> ? ∊ {1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3}
[[1,3,4,5,6,7],[2]]
=> [[1,2,4,5,6,7],[3]]
=> [3,1,2,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,4,5,6,7],[3]]
=> [[1,2,3,5,6,7],[4]]
=> [4,1,2,3,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,3,5,6,7],[4]]
=> [[1,2,3,4,6,7],[5]]
=> [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
[[1,2,3,4,6,7],[5]]
=> [[1,2,3,4,5,7],[6]]
=> [6,1,2,3,4,5,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
The following 10 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001964The interval resolution global dimension of a poset. St001868The number of alignments of type NE of a signed permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001845The number of join irreducibles minus the rank of a lattice. St001866The nesting alignments of a signed permutation. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001396Number of triples of incomparable elements in a finite poset.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!