Identifier
Identifier
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.
References
[1] Haiman, M. D. Conjectures on the quotient ring by diagonal invariants MathSciNet:1256101
[2] Armstrong, D., Reiner, V., Rhoades, B. Parking spaces MathSciNet:3281144
Created
Jun 25, 2017 at 19:50 by Christian Stump
Updated
Jun 25, 2017 at 19:50 by Christian Stump