Compatibility of Real-Rooted Polynomials with Mixed Signs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909279008587776 |
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| author | Leake, Jonathan Ryder, Nick |
| author_facet | Leake, Jonathan Ryder, Nick |
| contents | We characterize compatible families of real-rooted polynomials, allowing both positive and negative leading coefficients. Our characterization naturally generalizes the same-sign characterization used by Chudnovsky and Seymour in their famous 2007 paper proving the real-rootedness of independence polynomials of claw-free graphs, thus fully settling a question left open in their paper. Our methods are generally speaking elementary, utilizing mainly linear algebra and the established theory of interlacing polynomials, with a bit of invariant theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compatibility of Real-Rooted Polynomials with Mixed Signs Leake, Jonathan Ryder, Nick Combinatorics 26C10, 05A20 We characterize compatible families of real-rooted polynomials, allowing both positive and negative leading coefficients. Our characterization naturally generalizes the same-sign characterization used by Chudnovsky and Seymour in their famous 2007 paper proving the real-rootedness of independence polynomials of claw-free graphs, thus fully settling a question left open in their paper. Our methods are generally speaking elementary, utilizing mainly linear algebra and the established theory of interlacing polynomials, with a bit of invariant theory. |
| title | Compatibility of Real-Rooted Polynomials with Mixed Signs |
| topic | Combinatorics 26C10, 05A20 |
| url | https://arxiv.org/abs/2407.16226 |