**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.

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]

[2]

**Haiman, M. D.***Conjectures on the quotient ring by diagonal invariants*MathSciNet:1256101[2]

**Armstrong, D., Reiner, V., Rhoades, B.***Parking spaces*MathSciNet:3281144Created

Jun 25, 2017 at 19:50 by

**Christian Stump**Updated

Jun 25, 2017 at 19:50 by

**Christian Stump**searching the database

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