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arXiv · 2312.03975

The classification of Boolean degree $1$ functions in high-dimensional finite vector spaces

Ferdinand Ihringer
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Abstract

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.

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Ferdinand Ihringer. 2024-05-26. The classification of Boolean degree $1$ functions in high-dimensional finite vector spaces. https://arxiv.org/abs/2312.03975

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