Identifier
Values
['A',1] => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 5
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 size of the largest ordinal summand in the poset.
The ordinal sum of two posets $P$ and $Q$ is the poset having elements $(p,0)$ and $(q,1)$ for $p\in P$ and $q\in Q$, and relations $(a,0) < (b,0)$ if $a < b$ in $P$, $(a,1) < (b,1)$ if $a < b$ in $Q$, and $(a,0) < (b,1)$.
This statistic is the maximal cardinality of a summand in the longest ordinal decomposition 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.