Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000177
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Mapping
St000177: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[2,0],[0]]
 => 0
[[2,0],[1]]
 => 0
[[2,0],[2]]
 => 0
[[1,1],[1]]
 => 0
[[3,0,0],[0,0],[0]]
 => 0
[[3,0,0],[1,0],[0]]
 => 1
[[3,0,0],[1,0],[1]]
 => 0
[[3,0,0],[2,0],[0]]
 => 1
[[3,0,0],[2,0],[1]]
 => 1
[[3,0,0],[2,0],[2]]
 => 0
[[3,0,0],[3,0],[0]]
 => 0
[[3,0,0],[3,0],[1]]
 => 0
[[3,0,0],[3,0],[2]]
 => 0
[[3,0,0],[3,0],[3]]
 => 0
[[2,1,0],[1,0],[0]]
 => 0
[[2,1,0],[1,0],[1]]
 => 0
[[2,1,0],[1,1],[1]]
 => 0
[[2,1,0],[2,0],[0]]
 => 0
[[2,1,0],[2,0],[1]]
 => 0
[[2,1,0],[2,0],[2]]
 => 0
[[2,1,0],[2,1],[1]]
 => 0
[[2,1,0],[2,1],[2]]
 => 0
[[1,1,1],[1,1],[1]]
 => 0
[[4,0,0,0],[0,0,0],[0,0],[0]]
 => 0
[[4,0,0,0],[1,0,0],[0,0],[0]]
 => 1
[[4,0,0,0],[1,0,0],[1,0],[0]]
 => 1
[[4,0,0,0],[1,0,0],[1,0],[1]]
 => 0
[[4,0,0,0],[2,0,0],[0,0],[0]]
 => 1
[[4,0,0,0],[2,0,0],[1,0],[0]]
 => 2
[[4,0,0,0],[2,0,0],[1,0],[1]]
 => 1
[[4,0,0,0],[2,0,0],[2,0],[0]]
 => 1
[[4,0,0,0],[2,0,0],[2,0],[1]]
 => 1
[[4,0,0,0],[2,0,0],[2,0],[2]]
 => 0
[[4,0,0,0],[3,0,0],[0,0],[0]]
 => 1
[[4,0,0,0],[3,0,0],[1,0],[0]]
 => 2
[[4,0,0,0],[3,0,0],[1,0],[1]]
 => 1
[[4,0,0,0],[3,0,0],[2,0],[0]]
 => 2
[[4,0,0,0],[3,0,0],[2,0],[1]]
 => 2
[[4,0,0,0],[3,0,0],[2,0],[2]]
 => 1
[[4,0,0,0],[3,0,0],[3,0],[0]]
 => 1
[[4,0,0,0],[3,0,0],[3,0],[1]]
 => 1
[[4,0,0,0],[3,0,0],[3,0],[2]]
 => 1
[[4,0,0,0],[3,0,0],[3,0],[3]]
 => 0
[[4,0,0,0],[4,0,0],[0,0],[0]]
 => 0
[[4,0,0,0],[4,0,0],[1,0],[0]]
 => 1
[[4,0,0,0],[4,0,0],[1,0],[1]]
 => 0
[[4,0,0,0],[4,0,0],[2,0],[0]]
 => 1
[[4,0,0,0],[4,0,0],[2,0],[1]]
 => 1
[[4,0,0,0],[4,0,0],[2,0],[2]]
 => 0
[[4,0,0,0],[4,0,0],[3,0],[0]]
 => 1
Description
The number of free tiles in the pattern. The ''tiling'' of a pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called ''tiles'', and each entry in a pattern belong to exactly one tile. A tile is ''free'' if it does not intersect any of the first and the last row.