Identifier
Values
['A',1] => ([],1) => ([],1) => ([(0,1)],2) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The Hamming dimension of a graph.
Let $H(n, k)$ be the graph whose vertices are the subsets of $\{1,\dots,n\}$, and $(u,v)$ being an edge, for $u\neq v$, if the symmetric difference of $u$ and $v$ has cardinality at most $k$.
This statistic is the smallest $n$ such that the graph is an induced subgraph of $H(n, k)$ for some $k$.
Map
cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.