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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.07020 |
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| _version_ | 1866911372834504704 |
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| author | Menges, Amelie |
| author_facet | Menges, Amelie |
| contents | Given n convex bodies in the real space of dimension d, we consider the set of homogeneous polynomials of degree d in n variables that can be represented as their volume polynomial. This set is a subset of the set of Lorentzian polynomials. Using our knowledge of operations that preserve the Lorentzian property, we give a complete classification of the cases when the two sets are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07020 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparing the sets of volume polynomials and Lorentzian Polynomials Menges, Amelie Combinatorics Algebraic Geometry Given n convex bodies in the real space of dimension d, we consider the set of homogeneous polynomials of degree d in n variables that can be represented as their volume polynomial. This set is a subset of the set of Lorentzian polynomials. Using our knowledge of operations that preserve the Lorentzian property, we give a complete classification of the cases when the two sets are equal. |
| title | Comparing the sets of volume polynomials and Lorentzian Polynomials |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2310.07020 |