论文标题
带有不同红衣主教的电路和Cocirtits的广义尖峰
Generalized spikes with circuits and cocircuits of different cardinalities
论文作者
论文摘要
我们认为具有属性的矩阵，即$ s $的地面集合的每个子集都包含在$ 2S $ - 元素电路中，并且大小$ t $的每个子集都包含在$ 2T $ - 元素的Cocircuit中。我们说这样的Matroid具有\ emph {$（s，2s，t，2t）$ - 属性}。如果将地面设置为成对，以使任何$ s $ pairs的结合是电路，并且任何$ t $ pairs的结合是一个cocircuit，则矩阵是\ emph {$（s，s，t）$ - spike}。我们的主要结果是，所有足够大的具有$（s，2s，t，2t）$ - 属性为$（s，t）$ - 尖峰的属性的矩形，概括了2019年结果，证明了$ s = t $的情况。我们还提供了一些$（s，t）$ - 尖峰的属性。
We consider matroids with the property that every subset of the ground set of size $s$ is contained in a $2s$-element circuit and every subset of size $t$ is contained in a $2t$-element cocircuit. We say that such a matroid has the \emph{$(s,2s,t,2t)$-property}. A matroid is an \emph{$(s,t)$-spike} if there is a partition of the ground set into pairs such that the union of any $s$ pairs is a circuit and the union of any $t$ pairs is a cocircuit. Our main result is that all sufficiently large matroids with the $(s,2s,t,2t)$-property are $(s,t)$-spikes, generalizing a 2019 result that proved the case where $s=t$. We also present some properties of $(s,t)$-spikes.
