Publication Date
1-7-2026
Document Type
Article
Organizational Units
College of Natural Science and Mathematics, Mathematics
Keywords
Parking function, Labeled forest, Generating function, Pollak's circle argument, Bijection
Abstract
In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the joint distribution of two statistics on parking functions and their counterparts on labeled forests. Our results on labeled forests also serve to explain the mysterious equidistribution between two seemingly unrelated statistics in parking functions recently identified by Stanley and Yin and give an explicit bijection between the two statistics. Extensions of our techniques are discussed, including joint distribution on further refinement of these new statistics.
Copyright Date
1-7-2026
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Rights Holder
Stephan Wagner, Catherine H. Yan, and Mei Yin
Provenance
Received from Elsevier
File Format
application/pdf
Language
English (eng)
Extent
30 pgs
File Size
1.05 MB
Publication Statement
Copyright is held by the Authors. User is responsible for all copyright compliance. This article was originally published as
Wagner, S., Yan, C. H., & Yin, M. (2026). Distribution of New Statistics of Parking Functions and their Generalizations. Advances in Applied Mathematics, 174. https://doi.org/10.1016/j.aam.2025.103026
Publication Title
Advances in Applied Mathematics
Volume
174
First Page
103026
ISSN
0196-8858
Recommended Citation
Wagner, Stephan; Yan, Catherine H.; and Yin, Mei, "Distribution of New Statistics of Parking Functions and their Generalizations" (2026). Mathematics: Faculty Scholarship. 59.
https://digitalcommons.du.edu/math_faculty/59
https://doi.org/10.1016/j.aam.2025.103026