Recursive properties of the characteristic polynomial of weighted lattices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913900211994624 |
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| author | Alfarano, Gianira N. Byrne, Eimear |
| author_facet | Alfarano, Gianira N. Byrne, Eimear |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07567 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Recursive properties of the characteristic polynomial of weighted lattices Alfarano, Gianira N. Byrne, Eimear Combinatorics Information Theory 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. |
| title | Recursive properties of the characteristic polynomial of weighted lattices |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2305.07567 |