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On Cycles in Multiset Permutations, Parking Functions, and Related Structures

Authors Calum Buchanan , Fabian Burghart , Stephan Wagner , Mei Yin

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Generating functions
Keywords
  • parking function
  • multiset permutation
  • cycle type
  • cyclic point
  • terminal closer
  • equivalence of ensembles

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Abstract

In this paper we study cycles in multiset permutations and parking functions. As combinatorial objects, multiset permutations are essential building blocks for mappings and permutations, while parking functions lie between mappings and permutations. We take both algebraic and analytic views in our investigation and present exact as well as asymptotic results. We point to a surprising correspondence between two statistics on multiset permutations, terminal closers and cyclic points, shedding light on the combinatorial structure.

Cite As Get BibTex

Calum Buchanan, Fabian Burghart, Stephan Wagner, and Mei Yin. On Cycles in Multiset Permutations, Parking Functions, and Related Structures. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.AofA.2026.16

Author Details

Calum Buchanan
  • Department of Mathematics, University of Denver, Denver, CO 80208, USA
Fabian Burghart
  • Institute of Discrete Mathematics, TU Graz, Steyrergasse 30, 8010 Graz, Austria
Stephan Wagner
  • Institute of Discrete Mathematics, TU Graz, Steyrergasse 30, 8010 Graz, Austria
  • Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden
Mei Yin
  • Department of Mathematics, University of Denver, Denver, CO 80208, USA

Funding

  • Burghart, Fabian: Supported by the Austrian Science Fund (FWF) [10.55776/F1002].
  • Wagner, Stephan: Supported by the Swedish research council (VR), grant 2022-04030.
  • Yin, Mei: Supported by the Simons Travel Support for Mathematicians Grant 00007227.

Acknowledgements

The authors thank J. E. Paguyo, Martin Rubey, and Richard Stanley for helpful discussions.

References

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