2021/04/26 by Byrne, Eimear, Ceria, Michela, Ionica, Sorina +1 · 1 citation
#05A30 #05B35 #11T71 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.12463
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 q-polymatroid and outline several of its properties.