English

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 qq-matroids, the qq-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 qq-analogue of matroid union we come to a definition of the direct sum of qq-matroids. As a motivation for this definition, we show it has some desirable properties.

Keywords

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}
}