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 $n \geq n_0(k, q)$, a problem going back to a work by Cameron and Liebler from 1982. 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.

翻译：我们分类了在$q$元域上$n$维向量空间中$k$-子空间的布尔度$1$函数（也称为Cameron-Liebler类），其中$n \geq n_0(k, q)$。该问题可追溯至1982年Cameron与Liebler的开创性工作。这一结果同时表明，当$n \geq n_0(k, q)$时，关于$k$-子空间的两相交集不存在。我们的主要工具是几何格上的Ramsey理论。