Weighted Subspace Designs from $q$-Polymatroids
Combinatorics
2022-11-23 v4
Abstract
The Assmus-Mattson theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs. In this work we present a further two-fold generalisation: first from matroids to polymatroids and also from sets to vector spaces. To achieve this, we introduce the characteristic polynomial of a -polymatroid and outline several of its properties.
Cite
@article{arxiv.2104.12463,
title = {Weighted Subspace Designs from $q$-Polymatroids},
author = {Eimear Byrne and Michela Ceria and Sorina Ionica and Relinde Jurrius},
journal= {arXiv preprint arXiv:2104.12463},
year = {2022}
}