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Large Deviation Principles for Pattern-Avoiding Permutations, and Limit Shapes for Constrained Mallows Permutations

Authors: Thomas Budzinski, Victor Dubach, Valentin Féray, Mohamed Slim Kammoun, and Mylene Maïda

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


Abstract
We study Mallows random permutations conditioned to avoid a given pattern α of length 3, for which we find limit shapes in the space of permutons when the bias parameter is of the form e^(β/n). Along the way, we provide parametrizations for α-avoiding permutons, and establish large deviation principles for uniform α-avoiding permutations.

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Thomas Budzinski, Victor Dubach, Valentin Féray, Mohamed Slim Kammoun, and Mylene Maïda. Large Deviation Principles for Pattern-Avoiding Permutations, and Limit Shapes for Constrained Mallows Permutations. 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. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{budzinski_et_al:LIPIcs.AofA.2026.18,
  author =	{Budzinski, Thomas and Dubach, Victor and F\'{e}ray, Valentin and Kammoun, Mohamed Slim and Ma\"{i}da, Mylene},
  title =	{{Large Deviation Principles for Pattern-Avoiding Permutations, and Limit Shapes for Constrained Mallows Permutations}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{18:1--18:16},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-262895},
  doi =		{10.4230/LIPIcs.AofA.2026.18},
  annote =	{Keywords: Permutations, Pattern avoidance, Large deviations, Mallows distribution}
}
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