The classification of Boolean degree $1$ functions in high-dimensional finite vector spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917675399118848 |
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| author | Ihringer, Ferdinand |
| author_facet | Ihringer, Ferdinand |
| contents | We classify the Boolean degree $1$ functions of $k$-spaces in a vector space of dimension $n$ (also known as Cameron-Liebler classes) over the field with $q$ elements for $n \geq n_0(k, q)$. This also implies that two-intersecting sets with respect to $k$-spaces do not exist for $n \geq n_0(k, q)$. Our main ingredient is the Ramsey theory for geometric lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03975 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The classification of Boolean degree $1$ functions in high-dimensional finite vector spaces Ihringer, Ferdinand Combinatorics Discrete Mathematics We classify the Boolean degree $1$ functions of $k$-spaces in a vector space of dimension $n$ (also known as Cameron-Liebler classes) over the field with $q$ elements for $n \geq n_0(k, q)$. This also implies that two-intersecting sets with respect to $k$-spaces do not exist for $n \geq n_0(k, q)$. Our main ingredient is the Ramsey theory for geometric lattices. |
| title | The classification of Boolean degree $1$ functions in high-dimensional finite vector spaces |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2312.03975 |