Recursive properties of the characteristic polynomial of weighted lattices
Abstract
In this paper, we describe properties of the characteristic polynomial of a weighted lattice and show that it has a recursive description, which we use to obtain results on the critical exponent of $q$-polymatroids. We give a Critical Theorem for representable $q$-polymatroids and we provide a lower bound on the critical exponent. We show that $q$-polymatroids arising from certain families of rank-metric codes attain this lower bound.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Coding theory and cryptography
Advanced Graph Theory Research
Publication details
- Journal / source
- HAL (Le Centre pour la Communication Scientifique Directe)
- Publication date
- 15 January 2026
- Language
- EN
- Document type
- Preprint