混合分拆函数与指数有界边连通秩
Mixed partition functions and exponentially bounded edge-connection rank
摘要：
我们研究图参数，其相关的边连接矩阵具有指数有界的秩增长。我们的主要结果是一个明确的建设一大类图参数与此属性，我们称之为混合分拆函数。混合分拆函数可以被看作顶点模型的分拆函数的推广，如de la Harpe和Jones所介绍的[P.de la Harpe，V.F.R. Jones，Graph invariants related to statistical mechanical models：examples and problems，Journal of Combinatorial Theory，Series B 57（1993）207- 227]，它们与正交辛超群的不变量理论有关。此外，我们表明，一个单图的特征多项式的评价是混合分拆函数的例子，回答一个问题的德拉Harpe和琼斯。
英文摘要：
We study graph parameters whose associated edge-connection matrices have exponentially bounded rank growth. Our main result is an explicit construction of a large class of graph parameters with this property that we call mixed partition functions. Mixed partition functions can be seen as a generalization of partition functions of vertex models, as introduced by de la Harpe and Jones, [P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: examples and problems, Journal of Combinatorial Theory, Series B 57 (1993) 207--227] and they are related to invariant theory of orthosymplectic supergroup. We moreover show that evaluations of the characteristic polynomial of a simple graph are examples of mixed partition functions, answering a question of de la Harpe and Jones.
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。
