论文标题
$ i_4 $ free和三角形的二进制矩阵的结构
The structure of $I_4$-free and triangle-free binary matroids
论文作者
论文摘要
一个简单的二进制矩阵称为$ i_4 $ free，如果其排名4的公寓都不是独立的集合。这些对象可以等效地定义为$ pg（n-1,2）$中的集合$ e $，$ | e \ cap f | $不是任何四维平面$ f $的基础。我们证明了一个分解定理，可以准确确定所有$ i_4 $ free和三角形的矩阵的结构。特别是，我们的定理意味着$ i_4 $ free和三角形的矩形最多具有$ 2 $的关键数字。
A simple binary matroid is called $I_4$-free if none of its rank-4 flats are independent sets. These objects can be equivalently defined as the sets $E$ of points in $PG(n-1,2)$ for which $|E \cap F|$ is not a basis of $F$ for any four-dimensional flat $F$. We prove a decomposition theorem that exactly determines the structure of all $I_4$-free and triangle-free matroids. In particular, our theorem implies that the $I_4$-free and triangle-free matroids have critical number at most $2$.
