Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000681
Mapping
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0]
 => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 1
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 1
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [2,1,1]
 => [1,1]
 => 1
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,2]
 => [2]
 => 1
[1,1,1,0,1,0,0,0]
 => [3,4,1,2] => [2,2]
 => [2]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [3,1,1]
 => [1,1]
 => 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,3,4] => [3,1,1]
 => [1,1]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [2,2,1]
 => [2,1]
 => 0
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [3,1,1]
 => [1,1]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,2,3,5] => [3,1,1]
 => [1,1]
 => 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,2,3] => [2,2,1]
 => [2,1]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [2,2,1]
 => [2,1]
 => 0
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,2,1]
 => [2,1]
 => 0
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [3,2]
 => [2]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,3,4] => [3,2]
 => [2]
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [3,1,1]
 => [1,1]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,2]
 => [2]
 => 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,1,3] => [3,2]
 => [2]
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,2,4,5] => [3,1,1]
 => [1,1]
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,1,2,5,4] => [3,2]
 => [2]
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [3,4,1,2,5] => [2,2,1]
 => [2,1]
 => 0
[1,1,1,0,1,0,0,1,0,0]
 => [3,4,1,5,2] => [3,2]
 => [2]
 => 1
[1,1,1,0,1,1,0,0,0,0]
 => [3,5,1,2,4] => [3,2]
 => [2]
 => 1
[1,1,1,1,0,0,1,0,0,0]
 => [4,1,5,2,3] => [3,2]
 => [2]
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 4
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,4,6,5] => [2,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [2,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,2,3,5,6,4] => [3,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,2,3,6,4,5] => [3,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [2,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,2,4,3,6,5] => [2,2,1,1]
 => [2,1,1]
 => 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [3,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,2,4,5,6,3] => [4,1,1]
 => [1,1]
 => 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,2,4,6,3,5] => [4,1,1]
 => [1,1]
 => 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,3,4,6] => [3,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,3,6,4] => [4,1,1]
 => [1,1]
 => 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,2,5,6,3,4] => [2,2,1,1]
 => [2,1,1]
 => 3
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,2,6,3,4,5] => [4,1,1]
 => [1,1]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [2,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => [2,2,1,1]
 => [2,1,1]
 => 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => [2,2,1,1]
 => [2,1,1]
 => 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,3,2,5,6,4] => [3,2,1]
 => [2,1]
 => 0
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,6,4,5] => [3,2,1]
 => [2,1]
 => 0
Description
The Grundy value of Chomp on Ferrers diagrams. Players take turns and choose a cell of the diagram, cutting off all cells below and to the right of this cell in English notation. The player who is left with the single cell partition looses. The traditional version is played on chocolate bars, see [1]. This statistic is the Grundy value of the partition, that is, the smallest non-negative integer which does not occur as value of a partition obtained by a single move.