Identifier
Values
[1] => ([],1) => ([],1) => ([],1) => 0
[1,1] => ([(0,1)],2) => ([],2) => ([],2) => 0
[2] => ([],2) => ([],1) => ([],1) => 0
[1,1,1] => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3) => 0
[1,2] => ([(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[2,1] => ([(0,2),(1,2)],3) => ([],2) => ([],2) => 0
[3] => ([],3) => ([],1) => ([],1) => 0
[1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([],4) => ([],4) => 0
[1,1,2] => ([(1,2),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[1,3] => ([(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([],3) => ([],3) => 0
[2,2] => ([(1,3),(2,3)],4) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[3,1] => ([(0,3),(1,3),(2,3)],4) => ([],2) => ([],2) => 0
[4] => ([],4) => ([],1) => ([],1) => 0
[1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([],5) => ([],5) => 0
[1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 2
[1,1,3] => ([(2,3),(2,4),(3,4)],5) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[1,4] => ([(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([],4) => ([],4) => 0
[2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[2,3] => ([(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([],3) => ([],3) => 0
[3,2] => ([(1,4),(2,4),(3,4)],5) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([],2) => ([],2) => 0
[5] => ([],5) => ([],1) => ([],1) => 0
[1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([],6) => ([],6) => 0
[1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 2
[1,1,4] => ([(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[1,5] => ([(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([],5) => ([],5) => 0
[2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 2
[2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[2,4] => ([(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([],4) => ([],4) => 0
[3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[3,3] => ([(2,5),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([],3) => ([],3) => 0
[4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => ([],2) => 0
[6] => ([],6) => ([],1) => ([],1) => 0
[1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 2
[1,1,5] => ([(4,5),(4,6),(5,6)],7) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[1,6] => ([(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([],6) => ([],6) => 0
[2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 2
[2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[2,5] => ([(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([],5) => ([],5) => 0
[3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => 2
[3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[3,4] => ([(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([],4) => ([],4) => 0
[4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => 1
[4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([],3) => ([],3) => 0
[5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => 0
[6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([],2) => ([],2) => 0
[7] => ([],7) => ([],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
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
weak duplicate order
Description
The weak duplicate order of the de-duplicate of a graph.
Let $G=(V, E)$ be a graph and let $N=\{ N_v | v\in V\}$ be the set of (distinct) neighbourhoods of $G$.
This map yields the poset obtained by ordering $N$ by reverse inclusion.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.