The direct sum of $q$-matroids
Combinatorics
2022-10-07 v4
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 -matroids, the -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 -analogue of matroid union we come to a definition of the direct sum of -matroids. As a motivation for this definition, we show it has some desirable properties.
Cite
@article{arxiv.2109.13637,
title = {The direct sum of $q$-matroids},
author = {Michela Ceria and Relinde Jurrius},
journal= {arXiv preprint arXiv:2109.13637},
year = {2022}
}