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Statistics of Parking Functions and Labeled Forests

Authors Stephan Wagner , Mei Yin

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Author Details

Stephan Wagner
  • Institute of Discrete Mathematics, TU Graz, Austria
  • Department of Mathematics, Uppsala University, Sweden
Mei Yin
  • Department of Mathematics, University of Denver, CO, USA

Funding

  • Wagner, Stephan: Supported by the Swedish research council (VR), grant 2022-04030.
  • Yin, Mei: Supported by the University of Denver’s Professional Research Opportunities for Faculty Fund 80369-145601.

Acknowledgements

The authors benefited from participation in the Workshop on Analytic and Probabilistic Combinatorics at the Banff International Research Station in November 2022 and also from participation in the 34th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms in Taipei in June 2023.

Cite AsGet BibTex

Stephan Wagner and Mei Yin. Statistics of Parking Functions and Labeled Forests. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.29

Abstract

In this paper we obtain some new results on the enumeration of parking functions and labeled forests. We introduce new statistics both for parking functions and for labeled forests that are connected to each other by means of a bijection. 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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Generating functions
Keywords
  • parking function
  • labeled forest
  • generating function
  • Pollak’s circle argument
  • bijection

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