On the Chow-rank of the permanent
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915212510101504 |
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| author | Xu, Rongyu Gnang, Edinah |
| author_facet | Xu, Rongyu Gnang, Edinah |
| contents | We derive Glynn's formula from Ryser's formula for the permanent. We further establish via an orbital argument that Glynn's formula yields an optimal row-homogeneous Chow-decomposition of the permanent. We introduce a method for upper-bounding the Chow-rank of polynomials. Our method is based upon the Fundamental Theorem of Symmetric Polynomials. Finally we derive a parametric description of rank revealing row-homogeneous Chow-decompositions of the permanent. Our result provides an alternative approach to the parametrization first obtained by Glynn. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05890 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Chow-rank of the permanent Xu, Rongyu Gnang, Edinah Computational Complexity We derive Glynn's formula from Ryser's formula for the permanent. We further establish via an orbital argument that Glynn's formula yields an optimal row-homogeneous Chow-decomposition of the permanent. We introduce a method for upper-bounding the Chow-rank of polynomials. Our method is based upon the Fundamental Theorem of Symmetric Polynomials. Finally we derive a parametric description of rank revealing row-homogeneous Chow-decompositions of the permanent. Our result provides an alternative approach to the parametrization first obtained by Glynn. |
| title | On the Chow-rank of the permanent |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2311.05890 |