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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 , Mylene Maïda

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LIPIcs.AofA.2026.18.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Permutations and combinations
  • Mathematics of computing → Convex optimization
Keywords
  • Permutations
  • Pattern avoidance
  • Large deviations
  • Mallows distribution

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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) https://doi.org/10.4230/LIPIcs.AofA.2026.18

Author Details

Thomas Budzinski
  • ENS de Lyon, CNRS, UMPA, France
Victor Dubach
  • Uppsala University, Sweden
Valentin Féray
  • Université de Lorraine, CNRS, IECL, F-54000 Nancy, France
Mohamed Slim Kammoun
  • Université de Poitiers, LMA, France
Mylene Maïda
  • Université de Lille, CNRS, Laboratoire Paul Painlevé, France

Funding

ANR project LOUCCCOUM (Large Objects Under Combinatorial Constraints and Outside Uniform Models, ANR-24-CE40-7809)

References

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