The direct sum of $q$matroids
Abstract
For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for $q$matroids, the $q$analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the reader. With the use of submodular functions and the $q$analogue of matroid union we come to a definition of the direct sum of $q$matroids. As a motivation for this definition, we show it has some desirable properties.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 DOI:
 10.48550/arXiv.2109.13637
 arXiv:
 arXiv:2109.13637
 Bibcode:
 2021arXiv210913637C
 Keywords:

 Mathematics  Combinatorics;
 05B35;
 05A30