- FindStat

Identifier

St000207: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [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
[5,1,1,1]=>99
[4,4]=>94
[4,3,1]=>54
[4,2,2]=>73
[4,2,1,1]=>64
[4,1,1,1,1]=>64
[3,3,2]=>42
[3,3,1,1]=>54
[3,2,2,1]=>42
[3,2,1,1,1]=>48
[3,1,1,1,1,1]=>29
[2,2,2,2]=>26
[2,2,2,1,1]=>25
[2,2,1,1,1,1]=>22
[2,1,1,1,1,1,1]=>8
[1,1,1,1,1,1,1,1]=>1
                    

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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.

References

[1] De Loera, Jesús A., McAllister, T. B. Vertices of Gelfand-Tsetlin polytopes MathSciNet:2096742

Created

May 19, 2014 at 11:32 by Per Alexandersson

Updated

May 29, 2015 at 17:10 by Martin Rubey