Identifier
Identifier
Values
['A',1] generating graphics... => 3
['A',2] generating graphics... => 16
['B',2] generating graphics... => 25
['G',2] generating graphics... => 49
['A',3] generating graphics... => 125
['B',3] generating graphics... => 343
['C',3] generating graphics... => 343
['A',4] generating graphics... => 1296
['B',4] generating graphics... => 6561
['C',4] generating graphics... => 6561
['D',4] generating graphics... => 2401
['F',4] generating graphics... => 28561
['A',5] generating graphics... => 16807
['B',5] generating graphics... => 161051
['C',5] generating graphics... => 161051
['D',5] generating graphics... => 59049
['A',6] generating graphics... => 262144
['B',6] generating graphics... => 4826809
['C',6] generating graphics... => 4826809
['D',6] generating graphics... => 1771561
['E',6] generating graphics... => 4826809
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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