Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001597
(load all 4 compositions to match this statistic)
Mapping
St001597: Skew partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => 1
[[2],[]]
 => 1
[[1,1],[]]
 => 1
[[2,1],[1]]
 => 2
[[3],[]]
 => 1
[[2,1],[]]
 => 1
[[3,1],[1]]
 => 2
[[2,2],[1]]
 => 1
[[3,2],[2]]
 => 2
[[1,1,1],[]]
 => 1
[[2,2,1],[1,1]]
 => 2
[[2,1,1],[1]]
 => 2
[[3,2,1],[2,1]]
 => 3
[[4],[]]
 => 1
[[3,1],[]]
 => 1
[[4,1],[1]]
 => 2
[[2,2],[]]
 => 2
[[3,2],[1]]
 => 1
[[4,2],[2]]
 => 2
[[2,1,1],[]]
 => 1
[[3,2,1],[1,1]]
 => 2
[[3,1,1],[1]]
 => 2
[[4,2,1],[2,1]]
 => 3
[[3,3],[2]]
 => 1
[[4,3],[3]]
 => 2
[[2,2,1],[1]]
 => 1
[[3,3,1],[2,1]]
 => 2
[[3,2,1],[2]]
 => 2
[[4,3,1],[3,1]]
 => 3
[[2,2,2],[1,1]]
 => 1
[[3,3,2],[2,2]]
 => 2
[[3,2,2],[2,1]]
 => 2
[[4,3,2],[3,2]]
 => 3
[[1,1,1,1],[]]
 => 1
[[2,2,2,1],[1,1,1]]
 => 2
[[2,2,1,1],[1,1]]
 => 2
[[3,3,2,1],[2,2,1]]
 => 3
[[2,1,1,1],[1]]
 => 2
[[3,2,2,1],[2,1,1]]
 => 3
[[3,2,1,1],[2,1]]
 => 3
[[4,3,2,1],[3,2,1]]
 => 4
[[5],[]]
 => 1
[[4,1],[]]
 => 1
[[5,1],[1]]
 => 2
[[3,2],[]]
 => 2
[[4,2],[1]]
 => 1
[[5,2],[2]]
 => 2
[[3,1,1],[]]
 => 1
[[4,2,1],[1,1]]
 => 2
[[4,1,1],[1]]
 => 2
Description
The Frobenius rank of a skew partition. This is the minimal number of border strips in a border strip decomposition of the skew partition.
Matching statistic: St000482
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000482: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => ([],1)
 => 1
[[2],[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[[2,1],[1]]
 => ([],2)
 => ([],2)
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
[[3,1],[1]]
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
[[3,2],[2]]
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
[[2,1,1],[1]]
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
[[3,2,1],[2,1]]
 => ([],3)
 => ([],3)
 => 3
[[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[4,1],[1]]
 => ([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[2,2],[]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[[3,2],[1]]
 => ([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[4,2],[2]]
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
[[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[3,2,1],[1,1]]
 => ([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[3,1,1],[1]]
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
[[4,2,1],[2,1]]
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
[[3,3],[2]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[4,3],[3]]
 => ([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[2,2,1],[1]]
 => ([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[3,3,1],[2,1]]
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[3,2,1],[2]]
 => ([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[4,3,1],[3,1]]
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
[[2,2,2],[1,1]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[3,3,2],[2,2]]
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
[[3,2,2],[2,1]]
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[4,3,2],[3,2]]
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
[[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
[[2,2,2,1],[1,1,1]]
 => ([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[2,2,1,1],[1,1]]
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
[[3,3,2,1],[2,2,1]]
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
[[2,1,1,1],[1]]
 => ([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[[3,2,2,1],[2,1,1]]
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
[[3,2,1,1],[2,1]]
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
[[4,3,2,1],[3,2,1]]
 => ([],4)
 => ([],4)
 => 4
[[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
[[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
[[5,1],[1]]
 => ([(1,4),(3,2),(4,3)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
[[3,2],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
[[4,2],[1]]
 => ([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
[[5,2],[2]]
 => ([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => 2
[[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
[[4,2,1],[1,1]]
 => ([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
[[4,1,1],[1]]
 => ([(0,3),(1,4),(4,2)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => 2
Description
The (zero)-forcing number of a graph. This is the minimal number of vertices initially coloured black, such that eventually all vertices of the graph are coloured black when using the following rule: when $u$ is a black vertex of $G$, and exactly one neighbour $v$ of $u$ is white, then colour $v$ black.