摘要
令N表示满足如下条件的数对(k,l)∈(N∪{∞})^(2)全体:存在一个无穷电网络,其上的绑定生成森林几乎处处有l棵树,而其上的自由生成森林以正概率有k棵树.证明了N={(k,l)∈N^(2)|k≤l}∪{(∞,∞)}∪{(k,∞)|k∈N}.
Let N be the set of pairs( k,l) ∈( N ∪ {∞})^(2) such that on some infinite electric network,wired spanning forest has l trees almost surely, while free spanning forest has k trees with positive probability. It’s proved that N = {(k,l) ∈ N^(2)| k≤ l} ∪ {(∞,∞) } ∪ {(k,∞) | k ∈ N }.
作者
黄始颖
刘玥琳
Huang Shiying;Liu Yuelin(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China;Department of Science and Technology,Tianjin University of Finance and Economicsy Tianjin 300222,China)
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2021年第2期27-30,共4页
Acta Scientiarum Naturalium Universitatis Nankaiensis
基金
Supported partially by CNNSF(11671216)
Hu Xiang Gaocengci Rencai Jujiao Gongcheng-Ch-uangxin Rencai(2019RS1057)。
