Recovering of the Grassmann graph from the subgraph of non-degenerate subspaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915714158297088 |
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| author | Pankov, Mark |
| author_facet | Pankov, Mark |
| contents | Let ${\mathbb F}$ be a (not necessarily finite) field. A subspace of the vector space ${\mathbb F}^n$ is called {\it non-degenerate} if it is not contained in a coordinate hyperplane. We show that the Grassmann graph of $k$-dimensional subspaces of ${\mathbb F}^n$, $1<k<n-1$, can be recovered from the subgraph of non-degenerate subspaces if $|{\mathbb F}|>n-k$. In the case when ${\mathbb F}={\mathbb F}_q$ is the field of $q$ elements, this subgraph is known as the graph of non-degenerate linear $[n,k]_q$ codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04125 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recovering of the Grassmann graph from the subgraph of non-degenerate subspaces Pankov, Mark Combinatorics Let ${\mathbb F}$ be a (not necessarily finite) field. A subspace of the vector space ${\mathbb F}^n$ is called {\it non-degenerate} if it is not contained in a coordinate hyperplane. We show that the Grassmann graph of $k$-dimensional subspaces of ${\mathbb F}^n$, $1<k<n-1$, can be recovered from the subgraph of non-degenerate subspaces if $|{\mathbb F}|>n-k$. In the case when ${\mathbb F}={\mathbb F}_q$ is the field of $q$ elements, this subgraph is known as the graph of non-degenerate linear $[n,k]_q$ codes. |
| title | Recovering of the Grassmann graph from the subgraph of non-degenerate subspaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.04125 |