Stable Polynomials via Undirected Colored Graphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915343778185216 |
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| author | Bickel, Kelly Hong, Yang |
| author_facet | Bickel, Kelly Hong, Yang |
| contents | This paper initiates a systematic study of connections between undirected colored graphs and associated two-variable stable polynomials obtained via Cauchy transform-type formulas. Examples of such stable polynomials have played crucial roles in other recent studies, though their general properties have remained rather opaque. Using linear algebra techniques, this paper characterizes when these stable polynomials have boundary zeros and studies the finer behavior, called contact order, of their zero sets near the guaranteed boundary zeros. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable Polynomials via Undirected Colored Graphs Bickel, Kelly Hong, Yang Complex Variables Functional Analysis Primary 32A08, Secondary 05C50, 32A40, 47A48 This paper initiates a systematic study of connections between undirected colored graphs and associated two-variable stable polynomials obtained via Cauchy transform-type formulas. Examples of such stable polynomials have played crucial roles in other recent studies, though their general properties have remained rather opaque. Using linear algebra techniques, this paper characterizes when these stable polynomials have boundary zeros and studies the finer behavior, called contact order, of their zero sets near the guaranteed boundary zeros. |
| title | Stable Polynomials via Undirected Colored Graphs |
| topic | Complex Variables Functional Analysis Primary 32A08, Secondary 05C50, 32A40, 47A48 |
| url | https://arxiv.org/abs/2506.12624 |