2000 character limit reached
Recursive properties of the characteristic polynomial of weighted lattices (2305.07567v3)
Published 12 May 2023 in math.CO, cs.IT, and math.IT
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.