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Matching statistic: St000859
Mapping
St000859: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 3
['A',2]
 => 16
['B',2]
 => 25
['G',2]
 => 49
['A',3]
 => 125
['B',3]
 => 343
['C',3]
 => 343
['A',4]
 => 1296
['B',4]
 => 6561
['C',4]
 => 6561
['D',4]
 => 2401
['F',4]
 => 28561
['A',5]
 => 16807
['B',5]
 => 161051
['C',5]
 => 161051
['D',5]
 => 59049
['A',6]
 => 262144
['B',6]
 => 4826809
['C',6]
 => 4826809
['D',6]
 => 1771561
['E',6]
 => 4826809
Description
The number of parking functions of a finite Cartan type. This is given by the size of the finite torus $Q / (h+1)Q$ where $Q$ is the root lattice. This is known to be equal to $(h+1)^n$ where $n$ is the rank and $h$ is the Coxeter number. See also [1, 2] for the Weyl group action on this finite torus.