- FindStat

Identifier

St001146: Finite Cartan types ⟶ ℤ

Values

=>
                            Cc0022;cc-rep
                            
                            
                            

                        ['A',1]=>2
['A',2]=>5
['B',2]=>7
['G',2]=>11
['A',3]=>12
['B',3]=>24
['C',3]=>24
['A',4]=>27
['B',4]=>77
['C',4]=>77
['D',4]=>45
['F',4]=>237
['A',5]=>58
['B',5]=>238
['C',5]=>238
['D',5]=>158
['A',6]=>121
['B',6]=>723
['C',6]=>723
['D',6]=>531
['E',6]=>1273
['A',7]=>248
['B',7]=>2180
['C',7]=>2180
['D',7]=>1732
['E',7]=>17636
                    

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

click to show known generating functions

Description

The number of Grassmannian elements in the Coxeter group of the given type.
An element is Grassmannian if it has at most one descent.

Code

def statistic(C):
    return CoxeterGroup(C, implementation='coxeter3').grassmannian_elements().cardinality()

Created

Apr 19, 2018 at 00:24 by Martin Rubey

Updated

Apr 19, 2018 at 00:24 by Martin Rubey