Identifier
Values
[] => ([],1) => [2] => 0
[[]] => ([(0,1)],2) => [3] => 0
[[],[]] => ([(0,2),(1,2)],3) => [3,2] => 1
[[[]]] => ([(0,2),(2,1)],3) => [4] => 0
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => [7] => 0
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => [7] => 0
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 1
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => [5] => 0
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 0
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 0
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => [5,2] => 1
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [6] => 0
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 1
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [7] => 0
[[[[[[[]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 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
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight.
Given $\lambda$ count how many integer partitions $w$ (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.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.