Vector Parking Functions and Tree Inversions

Overview

We find a depth-first search version of Dhar's burning algorithm that gives a bijection between the parking functions of a multigraph and its spanning trees. Thus we extend a result by Perkinson, Yang and Yu in response to a problem posed by Stanley. We also find another variant of this algorithm which gives a bijection between vector parking functions and labeled spanning trees closely related to the rooted planar trees. Both bijections have the goal of establishing a relation between the degree of a parking function, the ?-statistic for inversions, and the edge labelling of a tree. In addition, we find an intriguing formula for the number of vector parking functions in a special case of particular interest.

Awards (1)

• American Mathematical Society: Second Award of $200 $200

Competition history

• ISEF 2015 Category not listed · Entry MATH046I

Resources

• ISEF abstract page ↗

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