Talk: Ragnar Freij-Hollanti (October 31, 2025 at 11:00 AM, Seminar room N2409)

Derived and hypergraphical matroids

Ragnar Freij-Hollanti

Aalto University

 

Abstract:

Matroids provide a powerful framework for understanding dependence structures occurring in many fields of mathematics, in particular in coding theory and graph theory. To any linear (n,k) code one can associate a linear matroid, describing the dependences between coordinates, but also a represented derived matroid, describing the dependences between minimal support dual codewords. Notably, two codes can have the same linear matroid without having the same represented derived matroid. In this work, we propose a definition of a combinatorial derived matroid, associated to any matroid regardless of its representations, and present some of its fundamental properties. We also show how this definition generalizes to a hypergraphical matroid, associated to every hypergraph.

Biography:

Ragnar Freij-Hollanti is a Senior University lecturer at Aalto University in Finland. He obtained his PhD in Mathematics in 2012, from Chalmers University of Technology in Sweden, and has previously been a postdoc at Aalto University and at TUM (2017-2018). His research is on the interplay between combinatorics and discrete geometry, in particular with applications to coding theory.