Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000207
Mapping
St000207: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 1
[3]
 => 4
[2,1]
 => 3
[1,1,1]
 => 1
[4]
 => 8
[3,1]
 => 7
[2,2]
 => 5
[2,1,1]
 => 4
[1,1,1,1]
 => 1
[5]
 => 16
[4,1]
 => 15
[3,2]
 => 12
[3,1,1]
 => 11
[2,2,1]
 => 7
[2,1,1,1]
 => 5
[1,1,1,1,1]
 => 1
[6]
 => 32
[5,1]
 => 31
[4,2]
 => 26
[4,1,1]
 => 26
[3,3]
 => 23
[3,2,1]
 => 17
[3,1,1,1]
 => 16
[2,2,2]
 => 12
[2,2,1,1]
 => 11
[2,1,1,1,1]
 => 6
[1,1,1,1,1,1]
 => 1
[7]
 => 64
[6,1]
 => 63
[5,2]
 => 54
[5,1,1]
 => 57
[4,3]
 => 45
[4,2,1]
 => 38
[4,1,1,1]
 => 42
[3,3,1]
 => 27
[3,2,2]
 => 33
[3,2,1,1]
 => 30
[3,1,1,1,1]
 => 22
[2,2,2,1]
 => 14
[2,2,1,1,1]
 => 16
[2,1,1,1,1,1]
 => 7
[1,1,1,1,1,1,1]
 => 1
[8]
 => 128
[7,1]
 => 127
[6,2]
 => 110
[6,1,1]
 => 120
[5,3]
 => 89
[5,2,1]
 => 74
Description
Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. Given $\lambda$ count how many ''integer compositions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has all vertices in integer lattice points.