Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000898
Mapping
St000898: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,0],[0,1]]
 => 1
[[0,1],[1,0]]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => 2
[[0,1,0],[1,0,0],[0,0,1]]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => 1
[[0,1,0],[1,-1,1],[0,1,0]]
 => 1
[[0,0,1],[1,0,0],[0,1,0]]
 => 2
[[0,1,0],[0,0,1],[1,0,0]]
 => 2
[[0,0,1],[0,1,0],[1,0,0]]
 => 3
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => 3
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => 4
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => 2
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => 3
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => 3
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => 4
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => 3
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => 4
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => 3
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => 3
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => 4
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => 2
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => 2
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => 2
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => 3
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => 3
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => 3
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => 4
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => 1
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => 2
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => 2
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => 3
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => 2
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => 1
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => 1
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => 2
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => 2
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => 3
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => 3
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => 4
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => 2
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => 2
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => 3
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => 3
Description
The number of maximal entries in the last diagonal of the monotone triangle. Consider the alternating sign matrix $$ \left(\begin{array}{rrrrr} 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & -1 & 1 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 \end{array}\right). $$ The corresponding monotone triangle is $$ \begin{array}{ccccccccc} 5 & & 4 & & 3 & & 2 & & 1 \\ & 5 & & 4 & & 3 & & 1 & \\ & & 5 & & 3 & & 1 & & \\ & & & 5 & & 3 & & & \\ & & & & 4 & & & & \end{array} $$ The first entry $1$ in the last diagonal is maximal, because rows are strictly decreasing and its left neighbour is $2$. Also, the entry $3$ in the last diagonal is maximal, because diagonals from north-west to south-east are weakly decreasing, and its north-west neighbour is also $3$. All other entries in the last diagonal are non-maximal, thus the statistic on this matrix is $2$. Conjecturally, this statistic is equidistributed with [[St000066]].