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Identifier
Values
=>
Cc0022;cc-rep
['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
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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