Talk by Martin Bergamin
Date: 23.02.22 Time: 15.00 - 16.00 Room: Y27H25
In this thesis we aim to study the basics of the theory of matroids and their q-analogs in terms of several axiomatic definitions. We support these definitions by providing easy examples in particular to highlighting the differences between the classical cases and their q-analogue counterparts. Furthermore, we outline the connections to other mathematical concepts such as linear codes and combinatorial designs that are described in the literature, in particular, we provide possible ways of constructions based on these objects. We also present a possibly new way of constructing q-matroids based on subspace design by slightly modifying an approach from a recent paper written by Byrne et al., although the viability of the construction to provide new q-matroids could not be shown. Finally, we briefly explain q-polymatroids by following the structure of matroids and q-matroids to mention the current direction of the topic.
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