Mutate The study of permutation patterns is a very active area of research and has connections to many other fields of mathematics as well as to computer science and physics. One of the main questions in the field is the enumeration problem: Given a particular set of permutations, how many permutations does the set have of each length? The main goal of this research group is to develop a novel algorithm which will aid researchers in finding structures in sets of permutations and use those structures to find generating functions to enumerate the set. Our research interests lead also into various topics in discrete mathematics and computer science.

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Recent Papers

Turning cycle restrictions into mesh patterns via Foata's fundamental transformation

Submitted • April 2023

Authors: Anders Claesson, Henning Ulfarsson

An adjacent q-cycle is a natural generalization of an adjacent transposition. We show that the number of adjacent q-cycles in a permutation maps to the sum of occurrences of two...

Pattern avoiding Motzkin paths are almost rational

Submitted • August 2021

Authors: Christian Bean, Antonio Bernini, Matteo Cervetti, Luca Ferrari

Using a recursive approach, we show that the generating function for sets of Motzkin paths avoiding a single (not necessarily consecutive) pattern is rational over x and the Catalan generating...

Automated Enumeration of Combinatorial Classes with Proof-Number Search

Submitted 2019 • September 2019

Authors: Ragnar Pall Ardal, Henning Ulfarsson, Yngvi Bjornsson

Enumerative combinatorics has traditionally been the domain of work for human mathematicians and has been applied, for instance with the probabilistic method, in computer science. One of the main problems...