- FindStat

Identifier

Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001286: Graphs ⟶ ℤ

Values

['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4

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$F_{1} = q$

$F_{2} = q^{2} + q^{3} + q^{4}$

Description

The annihilation number of a graph.
For a graph on

$m$ edges with degree sequence

$d_1\leq\dots\leq d_n$ , this is the largest number

$k\leq n$ such that

$\sum_{i=1}^k d_i \leq m$ .

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.

Map

to graph

Description

Returns the Hasse diagram of the poset as an undirected graph.