Permutation Patterns
A special issue of Axioms (ISSN 2075-1680).
Deadline for manuscript submissions: 20 February 2026 | Viewed by 79
Special Issue Editor
Special Issue Information
Dear Colleagues,
A tremendous amount of research has been devoted to the study of permutation patterns under various restrictions. In the past two decades, there has been an explosion of research on the topic of permutation containment, which largely aims to answer the following question: what is the optimal way to contain every element of a set of permutations?
This topic has been called the “superpattern problem” or “superpermutation problem” and can be further subdivided in a number of ways depending on how we define “containment”. As this pertains to the broader topic of “universal objects”, in the recent literature, these objects have been dubbed “universal permutations”. In all definitions, we seek the shortest length of such a universal permutation. In most circumstances, only bounds on the lengths can be found.
In this Special Issue, we seek to form a compendium of recent results in this fascinating field, with the goal of spreading awareness of the current state of permutation containment and encouraging further research and exploration. Special consideration will be given to contributions in the following areas:
- Those containing a subset of permutations as patterns, i.e., for each element of a subset of permutations, a subsequence exists that is order isomorphic to the permutation;
- Those containing a subset of permutations as vincular patterns, where some elements of an occurrence may be forced to be consecutive;
- Those containing a set of permutations as patterns in a circular permutation (or cyclic permutation);
- Relationships between circular patterns and standard patterns.
Any submission providing novel results on the various forms of pattern containment is welcome. With any luck, the additional attention paid to this new field will draw more researchers into the field.
Dr. Daniel Gray
Guest Editor
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Keywords
- universal permutations
- superpatterns
- superpermutations
- circular permutations
- permutation patterns
- pattern avoidance
- pattern containment
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