具有非奇异$N_2$的三重三元系
Threefold triple systems with nonsingular $N_2$
摘要：
关于图和超图的关联矩阵的秩与它们的组合结构之间的关系，已有许多结果。在这里，我们考虑广义关联矩阵$N_2$（定义为包含对的边缘）的一类自然超图：三元系与索引为3。这样的系统与非奇异$N_2$（在有理数）似乎是相当罕见的，但他们可以与PBD封闭构造。事实上，对于大的阶数$v$，获得了接近$\binom{v}{2}$的秩的范围。
英文摘要：
There are various results connecting ranks of incidence matrices of graphs and hypergraphs with their combinatorial structure. Here, we consider the generalized incidence matrix $N_2$ (defined by inclusion of pairs in edges) for one natural class of hypergraphs: the triple systems with index three. Such systems with nonsingular $N_2$ (over the rationals) appear to be quite rare, yet they can be constructed with PBD closure. In fact, a range of ranks near $\binom{v}{2}$ is obtained for large orders $v$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
