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Documents authored by Yin, Mei

Document
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.
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.AofA.2024.29
Statistics of Parking Functions and Labeled Forests

Authors: Stephan Wagner and Mei Yin

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

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.
Cite as

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)

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@InProceedings{wagner_et_al:LIPIcs.AofA.2024.29,
  author =	{Wagner, Stephan and Yin, Mei},
  title =	{{Statistics of Parking Functions and Labeled Forests}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.29},
  URN =		{urn:nbn:de:0030-drops-204648},
  doi =		{10.4230/LIPIcs.AofA.2024.29},
  annote =	{Keywords: parking function, labeled forest, generating function, Pollak’s circle argument, bijection}
}
Document
DOI: 10.4230/LIPIcs.AofA.2022.18
Parking Functions, Multi-Shuffle, and Asymptotic Phenomena

Authors: Mei Yin

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)

Abstract
Given a positive integer-valued vector u = (u_1, … , u_m) with u_1 < ⋯ < u_m, a u-parking function of length m is a sequence π = (π_1, … , π_m) of positive integers whose non-decreasing rearrangement (λ_1, … , λ_m) satisfies λ_i ≤ u_i for all 1 ≤ i ≤ m. We introduce a combinatorial construction termed a parking function multi-shuffle to generic u-parking functions and obtain an explicit characterization of multiple parking coordinates. As an application, we derive various asymptotic probabilistic properties of a uniform u-parking function of length m when u_i = cm+ib. The asymptotic scenario in the generic situation c > 0 is in sharp contrast with that of the special situation c = 0.
Cite as

Mei Yin. Parking Functions, Multi-Shuffle, and Asymptotic Phenomena. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{yin:LIPIcs.AofA.2022.18,
  author =	{Yin, Mei},
  title =	{{Parking Functions, Multi-Shuffle, and Asymptotic Phenomena}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{18:1--18:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.18},
  URN =		{urn:nbn:de:0030-drops-161041},
  doi =		{10.4230/LIPIcs.AofA.2022.18},
  annote =	{Keywords: Parking function, Multi-shuffle, Asymptotic expansion, Abel’s multinomial theorem}
}
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