Diameter preserving surjections in the geometry of matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2013
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| _version_ | 1866910314730094592 |
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| author | Huang, Wen-ling Havlicek, Hans |
| author_facet | Huang, Wen-ling Havlicek, Hans |
| contents | We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping $ϕ:Γ\toΓ'$ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of $Γ$ are at a distance equal to the diameter of $Γ$ if, and only if, their images are at a distance equal to the diameter of $Γ'$. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_1345 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Diameter preserving surjections in the geometry of matrices Huang, Wen-ling Havlicek, Hans Combinatorics Algebraic Geometry Rings and Algebras 51A50, 15A57 We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping $ϕ:Γ\toΓ'$ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of $Γ$ are at a distance equal to the diameter of $Γ$ if, and only if, their images are at a distance equal to the diameter of $Γ'$. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices). |
| title | Diameter preserving surjections in the geometry of matrices |
| topic | Combinatorics Algebraic Geometry Rings and Algebras 51A50, 15A57 |
| url | https://arxiv.org/abs/1304.1345 |