论文标题
局部注射式登机示射证明，用于增加跨越森林
A local injective proof of log-concavity for increasing spanning forests
论文作者
论文摘要
我们给出了强大的对数洞穴的加权版本的明确组合证明，以生成多项式，以增加有限简单图的跨越森林，配备了整个顶点的订购。与文献中的类似证据相反，我们的注射是本地的，因为它通过将单个边缘从一个森林移动到另一个森林而进行。在完整图的特定情况下，这给出了第一种未签名的stirling数字的对数洞穴的新组合证明，其中一对排列被转换为新对，通过在第一个排列中打破单个循环并在第二个排列中粘合两个周期，而其他所有观察者都没有触摸。
We give an explicit combinatorial proof of a weighted version of strong log-concavity for the generating polynomial of increasing spanning forests of a finite simple graph equipped with a total ordering of the vertices. In contrast to similar proofs in the literature, our injection is local in the sense that it proceeds by moving a single edge from one forest to the other. In the particular case of the complete graph, this gives a new combinatorial proof of log-concavity of unsigned Stirling numbers of the first kind where a pair of permutations is transformed into a new pair by breaking a single cycle in the first permutation and gluing two cycles in the second permutation, while all the other spectator cycles are left untouched.
