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Setwise Distinguishable Permutations

Author Ishay Haviv

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LIPIcs.MFCS.2026.83.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Permutations and combinations
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Graph coloring
Keywords
  • permutations
  • parameterized complexity
  • kernelization
  • coloring problems

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Abstract

A family of permutations of [n] is called setwise distinguishable if for every permutation in the family there exists a subset of [n] whose image under this permutation differs from its image under any other permutation in the family. We prove that there exists a setwise distinguishable family of 2^{(2-o(1))⋅n} permutations of [n]. The result is optimal up to the o(1) term in the exponent and is achieved through an explicit construction. As an application, we obtain nearly tight conditional lower bounds on the kernelization complexity of graph coloring problems parameterized by the vertex-deletion distance to split graphs. This improves a result of Jansen and Kratsch (Inf. Comput., 2013).

Cite As Get BibTex

Ishay Haviv. Setwise Distinguishable Permutations. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 83:1-83:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.83

Author Details

Ishay Haviv
  • The Academic College of Tel Aviv-Yaffo, Israel

Acknowledgements

We would like to thank Shoni Gilboa for fruitful discussions and the anonymous reviewers for useful feedback.

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