Induced Lorentzian and volume polynomials
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918486822879232 |
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| author | Eur, Christopher Nepal, Nutan Qin, Daniel |
| author_facet | Eur, Christopher Nepal, Nutan Qin, Daniel |
| contents | Suppose one has a party of $m$ people, whose expertise collectively covers $n$ topics. Given a subset $T$ of the topics, one wishes to form a panel of $|T|$ people from the party such that $T$ can be covered by assigning a distinct topic to each panel member with the expertise. We show that the numbers of such panels, as $T$ varies, form a Lorentzian polynomial. We achieve this by showing that a certain linear operator on polynomials, which we call the ``inducing operator'' for its connection to induced (poly)matroids, preserves Lorentzian polynomials and realizable volume polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05319 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Induced Lorentzian and volume polynomials Eur, Christopher Nepal, Nutan Qin, Daniel Combinatorics Suppose one has a party of $m$ people, whose expertise collectively covers $n$ topics. Given a subset $T$ of the topics, one wishes to form a panel of $|T|$ people from the party such that $T$ can be covered by assigning a distinct topic to each panel member with the expertise. We show that the numbers of such panels, as $T$ varies, form a Lorentzian polynomial. We achieve this by showing that a certain linear operator on polynomials, which we call the ``inducing operator'' for its connection to induced (poly)matroids, preserves Lorentzian polynomials and realizable volume polynomials. |
| title | Induced Lorentzian and volume polynomials |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.05319 |