Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000178
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Mapping
St000178: 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]]
 => 2
[[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]]
 => 2
[[4,0,0,0],[2,0,0],[2,0],[1]]
 => 2
[[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]]
 => 2
[[4,0,0,0],[3,0,0],[3,0],[1]]
 => 2
[[4,0,0,0],[3,0,0],[3,0],[2]]
 => 2
[[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
Number of free entries. 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 do not intersect any of the first and the last row. This statistic is the total number of entries that belong to a free tile.