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DOI: 10.4230/LIPIcs.AofA.2026.16

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

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

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)

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.

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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)

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@InProceedings{buchanan_et_al:LIPIcs.AofA.2026.16,
  author =	{Buchanan, Calum and Burghart, Fabian and Wagner, Stephan and Yin, Mei},
  title =	{{On Cycles in Multiset Permutations, Parking Functions, and Related Structures}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.16},
  URN =		{urn:nbn:de:0030-drops-262874},
  doi =		{10.4230/LIPIcs.AofA.2026.16},
  annote =	{Keywords: parking function, multiset permutation, cycle type, cyclic point, terminal closer, equivalence of ensembles}
}

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

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