ACA 2022

SPECIAL SESSION at the 27TH International Conference on Applications of Computer Algebra (ACA2022)

15-19 August 2022, Istanbul-Gebze, Turkey

A q-analogue in combinatorics is a generalization obtained by replacing "finite sets" with "finite dimensional vector spaces over the finite field GF(q)".

Matroid theory originates as a generalization of linear independence in vector spaces and represents a connection between algebraic and geometric topics.

This session focuses on the q-analogue of matroids, first anticipated by Crapo in his PhD Thesis and re-discovered by Jurrius and Pellikaan, motivated by the connection between q-matroids and rank-metric codes. Like their classical counterparts, q-matroids have a connection to several other mathematical objects in combinatorics, including rank-metric codes, subspace designs, and finite geometry.

Recently, a q-matroid community was formed, and many researchers showed interest in q-matroids and related topics: this session aims to join members from this community for the first time.

We wish to invite talks about recent results and developments in q-matroids and q-polymatroids, including but not restricted to:

• cryptomorphic definitions;

• constructions of examples and families of examples;

• q-analogues of results in structural matroid theory;

• polynomials associated to q-(poly)matroids;

• connections with rank-metric codes;

• results on subspace designs, including computations of parameters and proof of existence;

• connections with combinatorial topology and commutative algebra;

• q-systems and linear sets in finite geometry.

ORGANIZERS

Gianira Alfarano

Institute of Mathematics - University of Zurich - gianiranicoletta.alfarano@math.uzh.ch

Michela Ceria

Department of Mechanics, Mathematics and Management - Politecnico di Bari - michela.ceria@gmail.com

Relinde Jurrius

Faculty of Military Sciences - Netherlands Defence Academy - rpmj.jurrius@mindef.nl