Parking Functions

1. Definitions

2. Parking Functions and Dyck Paths

3. Examples

4. Properties

5. Conjectures

6. Statistics

We have the following 7 statistics in the database:

The number of lucky cars of the parking function.
The dinv of a parking function.
Sum of the entries.
The cosum of a parking function.
The number of primary dinversion pairs of a labelled dyck path corresponding to a....
The number of secondary dinversion pairs of the dyck path corresponding to a park....
The sum of the entries of a parking function minus its length.

7. Maps

We have the following 6 maps in the database:

to non-decreasing parking function
to car permutation
to inverse des composition
to labelling permutation
to Dyck path
to touch composition

8. References

[CARLSSON]   E. Carlsson and A. Mellit, A Proof of the Shuffle Conjecture, http://arxiv.org/pdf/1508.06239v1.pdf.

[HICKS]   A. Hicks, A Parking Function Bijection Suggested by the Haglund-Morse-Zabrocki Conjecture, University of California- San Diego, (2010).

[STAN]   R. Stanley, Parking Functions, http://math.mit.edu/~rstan/transparencies/parking.pdf.

ParkingFunctions (last edited 2015-12-21 22:31:11 by JessicaStriker)