- FindStat

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

Matching statistic: St000983

Mapping

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
St000983: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,0,1,0]
 => [1]
 => 10 => 10 => 2
[1,0,1,0,1,0]
 => [2,1]
 => 1010 => 0110 => 2
[1,0,1,1,0,0]
 => [1,1]
 => 110 => 110 => 2
[1,1,0,0,1,0]
 => [2]
 => 100 => 010 => 3
[1,1,0,1,0,0]
 => [1]
 => 10 => 10 => 2
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 101010 => 100110 => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 11010 => 10110 => 3
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => 100110 => 001110 => 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 10110 => 01110 => 2
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 1110 => 1110 => 2
[1,1,0,0,1,0,1,0]
 => [3,2]
 => 10100 => 10010 => 3
[1,1,0,0,1,1,0,0]
 => [2,2]
 => 1100 => 1010 => 4
[1,1,0,1,0,0,1,0]
 => [3,1]
 => 10010 => 00110 => 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => 1010 => 0110 => 2
[1,1,0,1,1,0,0,0]
 => [1,1]
 => 110 => 110 => 2
[1,1,1,0,0,0,1,0]
 => [3]
 => 1000 => 0010 => 3
[1,1,1,0,0,1,0,0]
 => [2]
 => 100 => 010 => 3
[1,1,1,0,1,0,0,0]
 => [1]
 => 10 => 10 => 2
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => 10101010 => 01100110 => 2
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => 1101010 => 0110110 => 3
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => 10011010 => 11000110 => 2
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => 1011010 => 1100110 => 2
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => 111010 => 110110 => 3
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => 10100110 => 01001110 => 3
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => 1100110 => 0101110 => 4
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => 10010110 => 10001110 => 2
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => 1010110 => 1001110 => 2
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => 110110 => 101110 => 3
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => 10001110 => 00011110 => 2
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => 1001110 => 0011110 => 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => 101110 => 011110 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => 11110 => 11110 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => 1010100 => 0110010 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => 110100 => 011010 => 4
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => 1001100 => 1100010 => 3
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => 101100 => 110010 => 3
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 11100 => 11010 => 4
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => 1010010 => 0100110 => 3
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => 110010 => 010110 => 4
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => 1001010 => 1000110 => 2
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => 101010 => 100110 => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => 11010 => 10110 => 3
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => 1000110 => 0001110 => 2
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => 100110 => 001110 => 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => 10110 => 01110 => 2
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => 1110 => 1110 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => 101000 => 010010 => 3
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 11000 => 01010 => 5
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => 100100 => 100010 => 3
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => 10100 => 10010 => 3

Description

The length of the longest alternating subword. This is the length of the longest consecutive subword of the form

$010...$ or of the form

$101...$ .

Matching statistic: St001816

Mapping

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001816: Standard tableaux ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 25%

Values

[1,0,1,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,0,1,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => ? = 2 - 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => ? = 3 - 2
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => ? = 2 - 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => ? = 2 - 2
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => ? = 2 - 2
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => ? = 3 - 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => ? = 4 - 2
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => ? = 2 - 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => ? = 3 - 2
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => ? = 2 - 2
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,8],[2,4,6,9,10]]
 => ? = 3 - 2
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[1,3,5,6,9],[2,4,7,8,10]]
 => ? = 2 - 2
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,6,8],[2,4,7,9,10]]
 => ? = 2 - 2
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[1,3,5,6,7],[2,4,8,9,10]]
 => ? = 3 - 2
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[1,3,4,7,9],[2,5,6,8,10]]
 => ? = 3 - 2
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[1,3,4,7,8],[2,5,6,9,10]]
 => ? = 4 - 2
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [[1,3,4,6,9],[2,5,7,8,10]]
 => ? = 2 - 2
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[1,3,4,6,8],[2,5,7,9,10]]
 => ? = 2 - 2
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[1,3,4,6,7],[2,5,8,9,10]]
 => ? = 3 - 2
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[1,3,4,5,9],[2,6,7,8,10]]
 => ? = 2 - 2
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 2 - 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[1,3,4,5,7],[2,6,8,9,10]]
 => ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[1,3,4,5,6],[2,7,8,9,10]]
 => ? = 2 - 2
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[1,2,5,7,9],[3,4,6,8,10]]
 => ? = 3 - 2
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[1,2,5,7,8],[3,4,6,9,10]]
 => ? = 4 - 2
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[1,2,5,6,9],[3,4,7,8,10]]
 => ? = 3 - 2
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[1,2,5,6,8],[3,4,7,9,10]]
 => ? = 3 - 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[1,2,5,6,7],[3,4,8,9,10]]
 => ? = 4 - 2
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[1,2,4,7,9],[3,5,6,8,10]]
 => ? = 3 - 2
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[1,2,4,7,8],[3,5,6,9,10]]
 => ? = 4 - 2
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[1,2,4,6,9],[3,5,7,8,10]]
 => ? = 2 - 2
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => ? = 2 - 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => ? = 3 - 2
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[1,2,4,5,9],[3,6,7,8,10]]
 => ? = 2 - 2
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => ? = 2 - 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => ? = 2 - 2
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => ? = 2 - 2
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[1,2,3,7,9],[4,5,6,8,10]]
 => ? = 3 - 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[1,2,3,7,8],[4,5,6,9,10]]
 => ? = 5 - 2
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[1,2,3,6,9],[4,5,7,8,10]]
 => ? = 3 - 2
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => ? = 3 - 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => ? = 4 - 2
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[1,2,3,5,9],[4,6,7,8,10]]
 => ? = 2 - 2
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => ? = 2 - 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[1,2,3,4,9],[5,6,7,8,10]]
 => ? = 3 - 2
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => ? = 3 - 2
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,9,10],[2,4,6,8,11,12]]
 => ? = 3 - 2
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [4,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,7,8,10],[2,4,6,9,11,12]]
 => ? = 3 - 2
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [[1,3,5,7,8,9],[2,4,6,10,11,12]]
 => ? = 3 - 2
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [[1,3,5,6,9,10],[2,4,7,8,11,12]]
 => ? = 3 - 2
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 3 - 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 2 - 2
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 2 - 2

Description

Eigenvalues of the top-to-random operator acting on a simple module. These eigenvalues are given in [1] and [3]. The simple module of the symmetric group indexed by a partition

$\lambda$ has dimension equal to the number of standard tableaux of shape

$\lambda$ . Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape

$\lambda$ ; this statistic gives all the eigenvalues of the operator acting on the module. This statistic bears different names, such as the type in [2] or eig in [3]. Similarly, the eigenvalues of the random-to-random operator acting on a simple module is [[St000508]].