Skip to main content

Research Repository

Advanced Search

All Outputs (5)

Permutations Avoiding Bipartite Partially Ordered Patterns Have a Regular Insertion Encoding (2024)
Journal Article
Bean, C., Nadeau, É., Pantone, J., & Ulfarsson, H. (2024). Permutations Avoiding Bipartite Partially Ordered Patterns Have a Regular Insertion Encoding. The Electronic Journal of Combinatorics, 31(3), Article P3.3. https://doi.org/10.37236/12686

We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to find combina... Read More about Permutations Avoiding Bipartite Partially Ordered Patterns Have a Regular Insertion Encoding.

Algorithmic coincidence classification of mesh patterns (2023)
Journal Article
Bean, C., Gudmundsson, B., Magnusson, T. K., & Ulfarsson, H. (2023). Algorithmic coincidence classification of mesh patterns. Information and Computation, https://doi.org/10.1016/j.ic.2023.105014

Permutations have connections to other mathematical objects such as Schubert varieties, sorting networks, and genome rearrangements. Often the connection is described in terms of patterns that are absent from the permutations. There can be ambiguity... Read More about Algorithmic coincidence classification of mesh patterns.

Using large random permutations to partition permutation classes (2022)
Journal Article
Bean, C., Nadeau, E., Pantone, J., & Ulfarsson, H. (2022). Using large random permutations to partition permutation classes. https://doi.org/10.2478/puma-2022-0006

<jats:title>Abstract</jats:title> <jats:p>Permutation classes are sets of permutations defined by the absence of certain substructures. In some cases permutation classes can be decomposed as unions of subclasses. We use combinatorial specifications a... Read More about Using large random permutations to partition permutation classes.

Enumeration of Permutation Classes and Weighted Labelled Independent Sets (2021)
Journal Article
Bean, C., Nadeau, É., & Ulfarsson, H. (2021). Enumeration of Permutation Classes and Weighted Labelled Independent Sets. Discrete Mathematics & Theoretical Computer Science, vol. 22 no. 2, Permutation Patterns 2019(Special issues), https://doi.org/10.46298/dmtcs.5995

In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding becomes a biject... Read More about Enumeration of Permutation Classes and Weighted Labelled Independent Sets.