Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000681
Mapping
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 1
[1,1]
 => 1
[3]
 => 2
[2,1]
 => 0
[1,1,1]
 => 2
[4]
 => 3
[3,1]
 => 3
[2,2]
 => 2
[2,1,1]
 => 3
[1,1,1,1]
 => 3
[5]
 => 4
[4,1]
 => 2
[3,2]
 => 0
[3,1,1]
 => 0
[2,2,1]
 => 0
[2,1,1,1]
 => 2
[1,1,1,1,1]
 => 4
[6]
 => 5
[5,1]
 => 5
[4,2]
 => 4
[4,1,1]
 => 1
[3,3]
 => 4
[3,2,1]
 => 1
[3,1,1,1]
 => 1
[2,2,2]
 => 4
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 5
[1,1,1,1,1,1]
 => 5
[7]
 => 6
[6,1]
 => 4
[5,2]
 => 3
[5,1,1]
 => 6
[4,3]
 => 0
[4,2,1]
 => 5
[4,1,1,1]
 => 0
[3,3,1]
 => 3
[3,2,2]
 => 3
[3,2,1,1]
 => 5
[3,1,1,1,1]
 => 6
[2,2,2,1]
 => 0
[2,2,1,1,1]
 => 3
[2,1,1,1,1,1]
 => 4
[1,1,1,1,1,1,1]
 => 6
[8]
 => 7
[7,1]
 => 7
[6,2]
 => 6
[6,1,1]
 => 7
[5,3]
 => 6
[5,2,1]
 => 7
[5,1,1,1]
 => 7
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.
Matching statistic: St000680
Mapping
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000680: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
[2]
 => [[2],[]]
 => ([(0,1)],2)
 => 2 = 1 + 1
[1,1]
 => [[1,1],[]]
 => ([(0,1)],2)
 => 2 = 1 + 1
[3]
 => [[3],[]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[2,1]
 => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => 1 = 0 + 1
[1,1,1]
 => [[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[4]
 => [[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[3,1]
 => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 4 = 3 + 1
[2,2]
 => [[2,2],[]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[2,1,1]
 => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 4 = 3 + 1
[1,1,1,1]
 => [[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[5]
 => [[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[4,1]
 => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 3 = 2 + 1
[3,2]
 => [[3,2],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 1 = 0 + 1
[3,1,1]
 => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 1 = 0 + 1
[2,2,1]
 => [[2,2,1],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 1 = 0 + 1
[2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 3 = 2 + 1
[1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[6]
 => [[6],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[5,1]
 => [[5,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 6 = 5 + 1
[4,2]
 => [[4,2],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 5 = 4 + 1
[4,1,1]
 => [[4,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 2 = 1 + 1
[3,3]
 => [[3,3],[]]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 5 = 4 + 1
[3,2,1]
 => [[3,2,1],[]]
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => 2 = 1 + 1
[3,1,1,1]
 => [[3,1,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 2 = 1 + 1
[2,2,2]
 => [[2,2,2],[]]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 5 = 4 + 1
[2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 5 = 4 + 1
[2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[7]
 => [[7],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[6,1]
 => [[6,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[5,2]
 => [[5,2],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[5,1,1]
 => [[5,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[4,3]
 => [[4,3],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[4,2,1]
 => [[4,2,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[4,1,1,1]
 => [[4,1,1,1],[]]
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[3,3,1]
 => [[3,3,1],[]]
 => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[3,2,2]
 => [[3,2,2],[]]
 => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[3,2,1,1]
 => [[3,2,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[2,2,2,1]
 => [[2,2,2,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[2,1,1,1,1,1]
 => [[2,1,1,1,1,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ? ∊ {0,0,0,3,3,3,3,4,4,5,5,6,6,6,6} + 1
[8]
 => [[8],[]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[7,1]
 => [[7,1],[]]
 => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[6,2]
 => [[6,2],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[6,1,1]
 => [[6,1,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[5,3]
 => [[5,3],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[5,2,1]
 => [[5,2,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[5,1,1,1]
 => [[5,1,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[4,4]
 => [[4,4],[]]
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[4,3,1]
 => [[4,3,1],[]]
 => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[4,2,2]
 => [[4,2,2],[]]
 => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[4,2,1,1]
 => [[4,2,1,1],[]]
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[3,3,2]
 => [[3,3,2],[]]
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[3,3,1,1]
 => [[3,3,1,1],[]]
 => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[3,2,2,1]
 => [[3,2,2,1],[]]
 => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[2,2,2,2]
 => [[2,2,2,2],[]]
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1],[]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? ∊ {0,0,1,1,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7} + 1
[9]
 => [[9],[]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[8,1]
 => [[8,1],[]]
 => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[7,2]
 => [[7,2],[]]
 => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[7,1,1]
 => [[7,1,1],[]]
 => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[6,3]
 => [[6,3],[]]
 => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[6,2,1]
 => [[6,2,1],[]]
 => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[6,1,1,1]
 => [[6,1,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[5,4]
 => [[5,4],[]]
 => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[5,3,1]
 => [[5,3,1],[]]
 => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[5,2,2]
 => [[5,2,2],[]]
 => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[5,2,1,1]
 => [[5,2,1,1],[]]
 => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[5,1,1,1,1]
 => [[5,1,1,1,1],[]]
 => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
[4,4,1]
 => [[4,4,1],[]]
 => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9)
 => ? ∊ {0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,6,6,6,8,8} + 1
Description
The Grundy value for Hackendot on posets. Two players take turns and remove an order filter. The player who is faced with the one element poset looses. This game is a slight variation of Chomp. This statistic is the Grundy value of the poset, that is, the smallest non-negative integer which does not occur as value of a poset obtained by a single move.