Identifier
Values
=>
Cc0022;cc-rep-0 Cc0014;cc-rep
['A',1]=>([],1)=>0 ['A',2]=>([(0,2),(1,2)],3)=>1 ['B',2]=>([(0,3),(1,3),(3,2)],4)=>1 ['G',2]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>1 ['A',3]=>([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>2
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 jump number of the poset.
A jump in a linear extension $e_1, \dots, e_n$ of a poset $P$ is a pair $(e_i, e_{i+1})$ so that $e_{i+1}$ does not cover $e_i$ in $P$. The jump number of a poset is the minimal number of jumps in linear extensions of a poset.
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.