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Matching statistic: St000208
Mapping
St000208: 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]
 => 3
[2,1]
 => 2
[1,1,1]
 => 1
[4]
 => 5
[3,1]
 => 4
[2,2]
 => 3
[2,1,1]
 => 2
[1,1,1,1]
 => 1
[5]
 => 7
[4,1]
 => 6
[3,2]
 => 4
[3,1,1]
 => 4
[2,2,1]
 => 2
[2,1,1,1]
 => 2
[1,1,1,1,1]
 => 1
[6]
 => 11
[5,1]
 => 10
[4,2]
 => 8
[4,1,1]
 => 7
[3,3]
 => 6
[3,2,1]
 => 4
[3,1,1,1]
 => 4
[2,2,2]
 => 3
[2,2,1,1]
 => 2
[2,1,1,1,1]
 => 2
[1,1,1,1,1,1]
 => 1
[7]
 => 15
[6,1]
 => 14
[5,2]
 => 12
[5,1,1]
 => 11
[4,3]
 => 8
[4,2,1]
 => 6
[4,1,1,1]
 => 7
[3,3,1]
 => 5
[3,2,2]
 => 5
[3,2,1,1]
 => 4
[3,1,1,1,1]
 => 4
[2,2,2,1]
 => 2
[2,2,1,1,1]
 => 2
[2,1,1,1,1,1]
 => 2
[1,1,1,1,1,1,1]
 => 1
[8]
 => 22
[7,1]
 => 21
[6,2]
 => 19
[6,1,1]
 => 17
[5,3]
 => 15
[5,2,1]
 => 9
Description
Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has only integer lattice points as vertices. See also [[St000205]], [[St000206]] and [[St000207]].