Processing math: 57%

Your data matches 21 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000993
(load all 2 compositions to match this statistic)
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => [2]
 => 1
([(0,1)],2)
 => [2]
 => [1,1]
 => 2
([],3)
 => [1,1,1]
 => [3]
 => 1
([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [2,2]
 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => 3
([],4)
 => [1,1,1,1]
 => [4]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [3,1]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [3,2]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [2,2,1]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [4,4]
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [2,2,2]
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,1,1,1]
 => 4
([],5)
 => [1,1,1,1,1]
 => [5]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [4,1]
 => 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [4,2]
 => 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [3,3]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [3,2,1]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [5,4]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [5,5]
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [3,2,2]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [6,6]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [4,4]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [5,5]
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [4,4,1]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [2,2,1,1]
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [2,2,2,1]
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [4,4,2]
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [4,4,4]
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [2,2,2,2]
 => 4
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St000297
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000297: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => [2]
 => 100 => 1
([(0,1)],2)
 => [2]
 => [1,1]
 => 110 => 2
([],3)
 => [1,1,1]
 => [3]
 => 1000 => 1
([(1,2)],3)
 => [2,1]
 => [2,1]
 => 1010 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [2,2]
 => 1100 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => 1110 => 3
([],4)
 => [1,1,1,1]
 => [4]
 => 10000 => 1
([(2,3)],4)
 => [2,1,1]
 => [3,1]
 => 10010 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [3,2]
 => 10100 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => 11000 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => 1100 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => 11000 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => 10110 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [2,2,1]
 => 11010 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [4,4]
 => 110000 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [2,2,2]
 => 11100 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,1,1,1]
 => 11110 => 4
([],5)
 => [1,1,1,1,1]
 => [5]
 => 100000 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [4,1]
 => 100010 => 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [4,2]
 => 100100 => 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => 101000 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => 110000 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => 10100 => 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => 101000 => 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [3,3]
 => 11000 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => 100110 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => 110000 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [3,2,1]
 => 101010 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => 110010 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [5,4]
 => 1010000 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [5,5]
 => 1100000 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [3,2,2]
 => 101100 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => 110010 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => 110100 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [6,6]
 => 11000000 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => 111000 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [4,4]
 => 110000 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => 11010 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => 110010 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => 11100 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [5,5]
 => 1100000 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [4,4,1]
 => 1100010 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => 111000 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => 110100 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => 101110 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [2,2,1,1]
 => 110110 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [2,2,2,1]
 => 111010 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [4,4,2]
 => 1100100 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [4,4,4]
 => 1110000 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [2,2,2,2]
 => 111100 => 4
Description
The number of leading ones in a binary word.
Matching statistic: St000326
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => 110 => 011 => 2 = 1 + 1
([(0,1)],2)
 => [2]
 => 100 => 001 => 3 = 2 + 1
([],3)
 => [1,1,1]
 => 1110 => 0111 => 2 = 1 + 1
([(1,2)],3)
 => [2,1]
 => 1010 => 0101 => 2 = 1 + 1
([(0,2),(1,2)],3)
 => [2,2]
 => 1100 => 0011 => 3 = 2 + 1
([(0,1),(0,2),(1,2)],3)
 => [3]
 => 1000 => 0001 => 4 = 3 + 1
([],4)
 => [1,1,1,1]
 => 11110 => 01111 => 2 = 1 + 1
([(2,3)],4)
 => [2,1,1]
 => 10110 => 01101 => 2 = 1 + 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => 11010 => 01011 => 2 = 1 + 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => 11100 => 00111 => 3 = 2 + 1
([(0,3),(1,2)],4)
 => [2,2]
 => 1100 => 0011 => 3 = 2 + 1
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => 11100 => 00111 => 3 = 2 + 1
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => 10010 => 01001 => 2 = 1 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => 10100 => 00101 => 3 = 2 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => 111100 => 001111 => 3 = 2 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => 11000 => 00011 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => 10000 => 00001 => 5 = 4 + 1
([],5)
 => [1,1,1,1,1]
 => 111110 => 011111 => 2 = 1 + 1
([(3,4)],5)
 => [2,1,1,1]
 => 101110 => 011101 => 2 = 1 + 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => 110110 => 011011 => 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => 111010 => 010111 => 2 = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => 111100 => 001111 => 3 = 2 + 1
([(1,4),(2,3)],5)
 => [2,2,1]
 => 11010 => 01011 => 2 = 1 + 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => 111010 => 010111 => 2 = 1 + 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => 11100 => 00111 => 3 = 2 + 1
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => 100110 => 011001 => 2 = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => 111100 => 001111 => 3 = 2 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => 101010 => 010101 => 2 = 1 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => 101100 => 001101 => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => 1111010 => 0101111 => 2 = 1 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => 1111100 => 0011111 => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => 110010 => 010011 => 2 = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => 101100 => 001101 => 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => 110100 => 001011 => 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => 11111100 => 00111111 => 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => 111000 => 000111 => 4 = 3 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => 111100 => 001111 => 3 = 2 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => 10100 => 00101 => 3 = 2 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => 101100 => 001101 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => 11000 => 00011 => 4 = 3 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => 1111100 => 0011111 => 3 = 2 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => 1011100 => 0011101 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => 111000 => 000111 => 4 = 3 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => 110100 => 001011 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => 100010 => 010001 => 2 = 1 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => 100100 => 001001 => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => 101000 => 000101 => 4 = 3 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => 1101100 => 0011011 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => 1111000 => 0001111 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => 110000 => 000011 => 5 = 4 + 1
Description
The position of the first one in a binary word after appending a 1 at the end. Regarding the binary word as a subset of {1,…,n,n+1} that contains n+1, this is the minimal element of the set.
Matching statistic: St001038
(load all 2 compositions to match this statistic)
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001038: Dyck paths ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => [1,1,0,0]
 => 1
([(0,1)],2)
 => [2]
 => [1,0,1,0]
 => 2
([],3)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 1
([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,0,1,0,1,0]
 => 3
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 4
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => 4
([(3,5),(3,6),(4,5),(4,6)],7)
 => [2,2,2,2,1,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
 => ? = 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [2,2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [2,2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
 => ? = 1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,3,2,2,1,1]
 => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
 => ? = 1
Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
Matching statistic: St001322
(load all 3 compositions to match this statistic)
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001322: Graphs ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
([],2)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 2
([],3)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 3
([],4)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 4
([],5)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 4
([(1,6),(2,5),(3,4)],7)
 => ([(1,6),(2,5),(3,4)],7)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
Description
The size of a minimal independent dominating set in a graph.
Matching statistic: St000733
(load all 2 compositions to match this statistic)
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => [2]
 => [[1,2]]
 => 1
([(0,1)],2)
 => [2]
 => [1,1]
 => [[1],[2]]
 => 2
([],3)
 => [1,1,1]
 => [3]
 => [[1,2,3]]
 => 1
([(1,2)],3)
 => [2,1]
 => [2,1]
 => [[1,3],[2]]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [2,2]
 => [[1,2],[3,4]]
 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => [[1],[2],[3]]
 => 3
([],4)
 => [1,1,1,1]
 => [4]
 => [[1,2,3,4]]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [3,1]
 => [[1,3,4],[2]]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [3,2]
 => [[1,2,5],[3,4]]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => [[1,2],[3,4]]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [[1,4],[2],[3]]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 4
([],5)
 => [1,1,1,1,1]
 => [5]
 => [[1,2,3,4,5]]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [4,1]
 => [[1,3,4,5],[2]]
 => 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => [[1,2,3,7],[4,5,6]]
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => [[1,2,5],[3,4]]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => [[1,2,3,7],[4,5,6]]
 => 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [3,2,1]
 => [[1,3,6],[2,5],[4]]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => [[1,5],[2],[3],[4]]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [2,2,2,1]
 => [[1,3],[2,5],[4,7],[6]]
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => 5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,4,4]
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => ? = 4
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,4,4]
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => ? = 4
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(3,5),(3,6),(4,5),(4,6)],7)
 => [2,2,2,2,1,1,1]
 => [7,4]
 => [[1,2,3,4,9,10,11],[5,6,7,8]]
 => ? = 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [2,2,2,2,2,1,1]
 => [7,5]
 => [[1,2,3,4,5,11,12],[6,7,8,9,10]]
 => ? = 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [2,2,2,2,2,1,1]
 => [7,5]
 => [[1,2,3,4,5,11,12],[6,7,8,9,10]]
 => ? = 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,1,1]
 => [6,4,1]
 => [[1,3,4,5,10,11],[2,7,8,9],[6]]
 => ? = 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2,1]
 => [6,5,1]
 => [[1,3,4,5,6,12],[2,8,9,10,11],[7]]
 => ? = 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,2,2,2,2,1]
 => [6,5,1]
 => [[1,3,4,5,6,12],[2,8,9,10,11],[7]]
 => ? = 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => [3,3,2,2,2]
 => [5,5,2]
 => [[1,2,5,6,7],[3,4,10,11,12],[8,9]]
 => ? = 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2
Description
The row containing the largest entry of a standard tableau.
Matching statistic: St000745
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000745: Standard tableaux ⟶ ℤResult quality: 56% ●values known / values provided: 56%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => [[1],[2]]
 => [[1,2]]
 => 1
([(0,1)],2)
 => [2]
 => [[1,2]]
 => [[1],[2]]
 => 2
([],3)
 => [1,1,1]
 => [[1],[2],[3]]
 => [[1,2,3]]
 => 1
([(1,2)],3)
 => [2,1]
 => [[1,3],[2]]
 => [[1,2],[3]]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [[1,2],[3,4]]
 => [[1,3],[2,4]]
 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 3
([],4)
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => [[1,2,3,4]]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [[1,4],[2],[3]]
 => [[1,2,3],[4]]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => [[1,2,4],[3,5]]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [[1,3,5],[2,4,6]]
 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [[1,2],[3,4]]
 => [[1,3],[2,4]]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [[1,3,5],[2,4,6]]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [[1,2,5],[3,4]]
 => [[1,3],[2,4],[5]]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8]]
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => [[1,4],[2,5],[3,6]]
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 4
([],5)
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [[1,2,3,4,5]]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [[1,5],[2],[3],[4]]
 => [[1,2,3,4],[5]]
 => 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => [[1,2,3,5],[4,6]]
 => 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [[1,3],[2,5],[4,7],[6]]
 => [[1,2,4,6],[3,5,7]]
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8]]
 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => [[1,2,4],[3,5]]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [[1,3],[2,5],[4,7],[6]]
 => [[1,2,4,6],[3,5,7]]
 => 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [[1,3,5],[2,4,6]]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8]]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [[1,3,6],[2,5],[4]]
 => [[1,2,4],[3,5],[6]]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7]]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8]]
 => [[1,2,4,6,8],[3,5,7,9]]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => [[1,2,5],[3,6],[4,7]]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7]]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => [[1,3,6],[2,4,7],[5,8]]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]
 => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => [[1,4,7],[2,5,8],[3,6,9]]
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8]]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [[1,2,5],[3,4]]
 => [[1,3],[2,4],[5]]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => [[1,3,5],[2,4,6],[7]]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => [[1,4],[2,5],[3,6]]
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [[1,2,9],[3,4],[5,6],[7,8]]
 => [[1,3,5,7],[2,4,6,8],[9]]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => [[1,4,7],[2,5,8],[3,6,9]]
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => [[1,3,6],[2,4,7],[5,8]]
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [[1,3,4,5],[2]]
 => [[1,2],[3],[4],[5]]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => [[1,3],[2,4],[5],[6]]
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [[1,2,3,7],[4,5,6]]
 => [[1,4],[2,5],[3,6],[7]]
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [[1,2,7],[3,4,10],[5,6],[8,9]]
 => [[1,3,5,8],[2,4,6,9],[7,10]]
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => [[1,5],[2,6],[3,7],[4,8]]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [[1,2,3,4,5]]
 => [[1],[2],[3],[4],[5]]
 => 5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8,11],[10]]
 => [[1,2,4,6,8,10],[3,5,7,9,11]]
 => ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [[1,2,5],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11]]
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8,11],[10]]
 => [[1,2,4,6,8,10],[3,5,7,9,11]]
 => ? = 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [[1,2,5],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11]]
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [[1,2,5],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11]]
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [[1,2,5],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11]]
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,1]
 => [[1,3,8],[2,5,11],[4,7],[6,10],[9]]
 => [[1,2,4,6,9],[3,5,7,10],[8,11]]
 => ? = 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [[1,2,5],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11]]
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,4,3]
 => [[1,2,3,7],[4,5,6,11],[8,9,10]]
 => [[1,4,8],[2,5,9],[3,6,10],[7,11]]
 => ? = 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
 => ? = 4
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [[1,2,5],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11]]
 => ? = 2
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
 => [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
 => ? = 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => [[1,5,9],[2,6,10],[3,7,11],[4,8,12]]
 => ? = 4
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,3,2,2]
 => [[1,2,7,11],[3,4,10],[5,6],[8,9]]
 => [[1,3,5,8],[2,4,6,9],[7,10],[11]]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,4,3]
 => [[1,2,3,7],[4,5,6,11],[8,9,10]]
 => [[1,4,8],[2,5,9],[3,6,10],[7,11]]
 => ? = 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,4,2,2]
 => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]]
 => [[1,3,5,9],[2,4,6,10],[7,11],[8,12]]
 => ? = 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,3,3,2]
 => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]]
 => [[1,3,6,9],[2,4,7,10],[5,8,11],[12]]
 => ? = 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8,11],[10]]
 => [[1,2,4,6,8,10],[3,5,7,9,11]]
 => ? = 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8,11],[10]]
 => [[1,2,4,6,8,10],[3,5,7,9,11]]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(3,5),(3,6),(4,5),(4,6)],7)
 => [2,2,2,2,1,1,1]
 => [[1,5],[2,7],[3,9],[4,11],[6],[8],[10]]
 => ?
 => ? = 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [2,2,2,2,2,1,1]
 => [[1,4],[2,6],[3,8],[5,10],[7,12],[9],[11]]
 => ?
 => ? = 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8,11],[10]]
 => [[1,2,4,6,8,10],[3,5,7,9,11]]
 => ? = 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [[1,3],[2,5],[4,7],[6,9],[8,11],[10]]
 => [[1,2,4,6,8,10],[3,5,7,9,11]]
 => ? = 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,1]
 => [[1,3,8],[2,5,11],[4,7],[6,10],[9]]
 => [[1,2,4,6,9],[3,5,7,10],[8,11]]
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,3,1,1]
 => [[1,4,5],[2,7,8],[3,10,11],[6],[9]]
 => [[1,2,3,6,9],[4,7,10],[5,8,11]]
 => ? = 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,1]
 => [[1,3,8],[2,5,11],[4,7],[6,10],[9]]
 => [[1,2,4,6,9],[3,5,7,10],[8,11]]
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [[1,2,11],[3,4],[5,6],[7,8],[9,10]]
 => [[1,3,5,7,9],[2,4,6,8,10],[11]]
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,3,2,1]
 => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]]
 => [[1,2,4,7,10],[3,5,8,11],[6,9,12]]
 => ? = 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,2,2,2]
 => [[1,2,9],[3,4,12],[5,6],[7,8],[10,11]]
 => [[1,3,5,7,10],[2,4,6,8,11],[9,12]]
 => ? = 2
Description
The index of the last row whose first entry is the row number in a standard Young tableau.
Matching statistic: St001184
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001184: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 86%
Values
([],2)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
([(0,1)],2)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2
([],3)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 1
([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 3
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 4
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 1
([(2,4),(3,4)],5)
 => [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
([(1,4),(2,4),(3,4)],5)
 => [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
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [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
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 5
([(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,1]
 => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,1]
 => [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2,2,2]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,3,2,2]
 => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,4,2,2]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,3,3,2]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
 => ? = 2
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(5,6)],7)
 => [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
([(4,6),(5,6)],7)
 => [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
([(3,6),(4,6),(5,6)],7)
 => [2,2,2,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(3,6),(4,5),(5,6)],7)
 => [2,2,2,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(4,5),(4,6),(5,6)],7)
 => [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
([(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [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
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,1]
 => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(3,5),(3,6),(4,5),(4,6)],7)
 => [2,2,2,2,1,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [2,2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,1,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
Description
Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra.
Matching statistic: St001481
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001481: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 86%
Values
([],2)
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
([(0,1)],2)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2
([],3)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 1
([(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 3
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 4
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 1
([(2,4),(3,4)],5)
 => [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
([(1,4),(2,4),(3,4)],5)
 => [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
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 1
([(1,4),(2,3),(3,4)],5)
 => [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
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 5
([(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,1]
 => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,1]
 => [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2,2,2]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [3,3,2,2,2]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,3,2,2]
 => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,4,2,2]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,3,3,2]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
 => ? = 2
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(5,6)],7)
 => [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
([(4,6),(5,6)],7)
 => [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
([(3,6),(4,6),(5,6)],7)
 => [2,2,2,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(3,6),(4,5),(5,6)],7)
 => [2,2,2,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(4,5),(4,6),(5,6)],7)
 => [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
([(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => [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
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [2,2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,1]
 => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,2,2,2,2]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(3,5),(3,6),(4,5),(4,6)],7)
 => [2,2,2,2,1,1,1]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [2,2,2,2,2,1,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [3,3,1,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [3,2,2,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [2,2,2,2,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1
Description
The minimal height of a peak of a Dyck path.
Matching statistic: St001803
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St001803: Standard tableaux ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 100%
Values
([],2)
 => [1,1]
 => [2]
 => [[1,2]]
 => 0 = 1 - 1
([(0,1)],2)
 => [2]
 => [1,1]
 => [[1],[2]]
 => 1 = 2 - 1
([],3)
 => [1,1,1]
 => [3]
 => [[1,2,3]]
 => 0 = 1 - 1
([(1,2)],3)
 => [2,1]
 => [2,1]
 => [[1,3],[2]]
 => 0 = 1 - 1
([(0,2),(1,2)],3)
 => [2,2]
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1]
 => [[1],[2],[3]]
 => 2 = 3 - 1
([],4)
 => [1,1,1,1]
 => [4]
 => [[1,2,3,4]]
 => 0 = 1 - 1
([(2,3)],4)
 => [2,1,1]
 => [3,1]
 => [[1,3,4],[2]]
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => [3,2]
 => [[1,2,5],[3,4]]
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => [2,2]
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [[1,4],[2],[3]]
 => 0 = 1 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 3 = 4 - 1
([],5)
 => [1,1,1,1,1]
 => [5]
 => [[1,2,3,4,5]]
 => 0 = 1 - 1
([(3,4)],5)
 => [2,1,1,1]
 => [4,1]
 => [[1,3,4,5],[2]]
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => [[1,2,3,7],[4,5,6]]
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => [2,2,1]
 => [3,2]
 => [[1,2,5],[3,4]]
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [4,3]
 => [[1,2,3,7],[4,5,6]]
 => 0 = 1 - 1
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [3,3]
 => [[1,2,3],[4,5,6]]
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [3,1,1]
 => [[1,4,5],[2],[3]]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 1 = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [3,2,1]
 => [[1,3,6],[2,5],[4]]
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 1 = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2,2,1]
 => [[1,3],[2,5],[4]]
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [2,2,2]
 => [[1,2],[3,4],[5,6]]
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => ? = 3 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => [[1,5],[2],[3],[4]]
 => 0 = 1 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [2,2,2,1]
 => [[1,3],[2,5],[4,7],[6]]
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => 4 = 5 - 1
([],6)
 => [1,1,1,1,1,1]
 => [6]
 => [[1,2,3,4,5,6]]
 => 0 = 1 - 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [5,1]
 => [[1,3,4,5,6],[2]]
 => 0 = 1 - 1
([(3,5),(4,5)],6)
 => [2,2,1,1,1]
 => [5,2]
 => [[1,2,5,6,7],[3,4]]
 => 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => [2,2,2,1,1]
 => [5,3]
 => [[1,2,3,7,8],[4,5,6]]
 => 0 = 1 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,2,2,2,1]
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [4,2]
 => [[1,2,5,6],[3,4]]
 => 0 = 1 - 1
([(2,5),(3,4),(4,5)],6)
 => [2,2,2,1,1]
 => [5,3]
 => [[1,2,3,7,8],[4,5,6]]
 => 0 = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => [2,2,2,1]
 => [4,3]
 => [[1,2,3,7],[4,5,6]]
 => 0 = 1 - 1
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [4,1,1]
 => [[1,4,5,6],[2],[3]]
 => 0 = 1 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [2,2,2,2,1]
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,1,1]
 => [6,4]
 => [[1,2,3,4,9,10],[5,6,7,8]]
 => ? = 1 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,1]
 => [4,3,2]
 => [[1,2,5,9],[3,4,8],[6,7]]
 => ? = 1 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => ? = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,1]
 => [4,3,3]
 => [[1,2,3,10],[4,5,6],[7,8,9]]
 => ? = 1 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [4,4,3]
 => [[1,2,3,7],[4,5,6,11],[8,9,10]]
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,3]
 => [4,4,4]
 => [[1,2,3,4],[5,6,7,8],[9,10,11,12]]
 => ? = 3 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,2,2,1]
 => [5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2,2,2,1]
 => [6,5]
 => [[1,2,3,4,5,11],[6,7,8,9,10]]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => ? = 2 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,1]
 => [5,4,1]
 => [[1,3,4,5,10],[2,7,8,9],[6]]
 => ? = 1 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => ? = 2 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,3,2,1]
 => [4,3,2]
 => [[1,2,5,9],[3,4,8],[6,7]]
 => ? = 1 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => ? = 2 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,1]
 => [4,3,3]
 => [[1,2,3,10],[4,5,6],[7,8,9]]
 => ? = 1 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3,2]
 => [4,4,3]
 => [[1,2,3,7],[4,5,6,11],[8,9,10]]
 => ? = 2 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2,2,2]
 => [5,5]
 => [[1,2,3,4,5],[6,7,8,9,10]]
 => ? = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [2,2,2,2,2,2]
 => [6,6]
 => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
 => ? = 2 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2]
 => [4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,2,2,2,2]
 => [5,5,1]
 => [[1,3,4,5,6],[2,8,9,10,11],[7]]
 => ? = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => ? = 2 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,3,3]
 => [3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,3,2,2]
 => [4,4,2]
 => [[1,2,5,6],[3,4,9,10],[7,8]]
 => ? = 2 - 1
Description
The maximal overlap of the cylindrical tableau associated with a tableau. A cylindrical tableau associated with a standard Young tableau T is the skew row-strict tableau obtained by gluing two copies of T such that the inner shape is a rectangle. The overlap, recorded in this statistic, equals max, where \ell denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux. In particular, the statistic equals 0, if and only if the last entry of the first row is larger than or equal to the first entry of the last row. Moreover, the statistic attains its maximal value, the number of rows of the tableau minus 1, if and only if the tableau consists of a single column.
The following 11 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000667The greatest common divisor of the parts of the partition. St001571The Cartan determinant of the integer partition. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001613The binary logarithm of the size of the center of a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001316The domatic number of a graph. St001621The number of atoms of a lattice. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000478Another weight of a partition according to Alladi. St000934The 2-degree of an integer partition. St001330The hat guessing number of a graph.