- FindStat

Identifier

St000206: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [1]=>0
[2]=>0
[1,1]=>0
[3]=>0
[2,1]=>0
[1,1,1]=>0
[4]=>0
[3,1]=>0
[2,2]=>0
[2,1,1]=>0
[1,1,1,1]=>0
[5]=>0
[4,1]=>0
[3,2]=>1
[3,1,1]=>0
[2,2,1]=>1
[2,1,1,1]=>0
[1,1,1,1,1]=>0
[6]=>0
[5,1]=>0
[4,2]=>3
[4,1,1]=>0
[3,3]=>1
[3,2,1]=>6
[3,1,1,1]=>0
[2,2,2]=>1
[2,2,1,1]=>1
[2,1,1,1,1]=>0
[1,1,1,1,1,1]=>0
[7]=>0
[6,1]=>0
[5,2]=>7
[5,1,1]=>0
[4,3]=>11
[4,2,1]=>16
[4,1,1,1]=>0
[3,3,1]=>17
[3,2,2]=>8
[3,2,1,1]=>8
[3,1,1,1,1]=>0
[2,2,2,1]=>7
[2,2,1,1,1]=>1
[2,1,1,1,1,1]=>0
[1,1,1,1,1,1,1]=>0
[8]=>0
[7,1]=>0
[6,2]=>15
[6,1,1]=>0
[5,3]=>31
[5,2,1]=>43
[5,1,1,1]=>0
[4,4]=>14
[4,3,1]=>53
[4,2,2]=>28
[4,2,1,1]=>31
[4,1,1,1,1]=>0
[3,3,2]=>39
[3,3,1,1]=>24
[3,2,2,1]=>30
[3,2,1,1,1]=>11
[3,1,1,1,1,1]=>0
[2,2,2,2]=>8
[2,2,2,1,1]=>8
[2,2,1,1,1,1]=>1
[2,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1]=>0
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

Number of non-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 non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Each value in this statistic is greater than or equal to corresponding value in St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..

References

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

Created

May 19, 2014 at 11:29 by Per Alexandersson

Updated

May 29, 2015 at 17:10 by Martin Rubey