论文标题
学位2布尔值在格拉曼图上的功能
Degree 2 Boolean Functions on Grassmann Graphs
论文作者
论文摘要
我们研究了vector Space $ \ mathbb {f} _q^n $在Grassmann图上的布尔度$ D $函数的存在。对于$ d = 1 $，已知几个不存在和分类结果，并且没有以$ n \ geq 5 $而闻名的非平凡示例。本文着重于提供有关$ d = 2 $的示例列表，尤其是$（n，k）=（6,3）$和$（n，k）=（8，4）$。 我们还讨论了与布尔函数分析，常规集/公平两部分/完美的2色，$ q $ - $ $ $ analogs设计和排列组的联系。特别是，这代表了Cameron-Liebler Line类的自然概括。
We investigate the existence of Boolean degree $d$ functions on the Grassmann graph of $k$-spaces in the vector space $\mathbb{F}_q^n$. For $d=1$ several non-existence and classification results are known, and no non-trivial examples are known for $n \geq 5$. This paper focusses on providing a list of examples on the case $d=2$ in general dimension and in particular for $(n, k)=(6,3)$ and $(n,k) = (8, 4)$. We also discuss connections to the analysis of Boolean functions, regular sets/equitable bipartitions/perfect 2-colorings in graphs, $q$-analogs of designs, and permutation groups. In particular, this represents a natural generalization of Cameron-Liebler line classes.
