On Infinity Type Hyperplane Arrangements and Convex Positive Bijections
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866914263786848256 |
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| author | Kumar, C. P. Anil |
| author_facet | Kumar, C. P. Anil |
| contents | In this article we prove in main Theorem A that any infinity type real hyperplane arrangement $\mathcal{H}_n^m$ (Definition 2.11) with the associated normal system $\mathcal{N}$ (Definitions [2.2,2.4] can be represented isomorphically (Definition 2.6) by another infinity type hyperplane arrangement $\tilde{\mathcal{H}}_n^m$ with a given associated normal system $\tilde{\mathcal{N}}$ if and only if the normal systems $\mathcal{N}$ and $\tilde{\mathcal{N}}$ are isomorphic, that is, there is a convex positive bijection (Definition 2.5) between a pair of associated sets of normal antipodal pairs of vectors of $\mathcal{N}$ and $\tilde{\mathcal{N}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_07030 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On Infinity Type Hyperplane Arrangements and Convex Positive Bijections Kumar, C. P. Anil Combinatorics Algebraic Topology Primary 52C35 In this article we prove in main Theorem A that any infinity type real hyperplane arrangement $\mathcal{H}_n^m$ (Definition 2.11) with the associated normal system $\mathcal{N}$ (Definitions [2.2,2.4] can be represented isomorphically (Definition 2.6) by another infinity type hyperplane arrangement $\tilde{\mathcal{H}}_n^m$ with a given associated normal system $\tilde{\mathcal{N}}$ if and only if the normal systems $\mathcal{N}$ and $\tilde{\mathcal{N}}$ are isomorphic, that is, there is a convex positive bijection (Definition 2.5) between a pair of associated sets of normal antipodal pairs of vectors of $\mathcal{N}$ and $\tilde{\mathcal{N}}$. |
| title | On Infinity Type Hyperplane Arrangements and Convex Positive Bijections |
| topic | Combinatorics Algebraic Topology Primary 52C35 |
| url | https://arxiv.org/abs/1711.07030 |