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arXiv · 2305.07567

Recursive properties of the characteristic polynomial of weighted lattices

Gianira N. Alfarano·Eimear Byrne
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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.

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Gianira N. Alfarano, Eimear Byrne. 2025-06-19. Recursive properties of the characteristic polynomial of weighted lattices. https://arxiv.org/abs/2305.07567

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