稳定集合分拆的伴随多项式和单峰性  

Adjoint Polynomials and Unimodality of Stable Set Partitons

作　　者：杨利民 杨娇艳 Yang Limin;Yang Jiaoyan(College of Mathematics and Computer,Dali University,Dali,Yunnan 671003,China)

机构地区：[1]大理大学数学与计算机学院,云南大理671003

出　　处：《大理大学学报》2024年第12期1-11,共11页Journal of Dali University

基　　金：国家自然科学基金项目(11861005);大理大学高层次人才科研启动基金项目(KY0719203410)。

摘　　要：为了研究稳定集合分拆的单峰性,提出伴随多项式的概念,并获得了几个图的伴随多项式。利用伴随多项式,证明了多种图的单峰性,如星形图、星形图的完全积、完全q-部图、(n-2)-正则图和(n-2)-正则图的完全积等。进一步,技巧性地计算了稳定集合分拆的所有个数。最后,推广了单峰性定理,并且导出几个例子,同时还推广了牛顿不等式的形式,得到了系列不等式。To study the unimodality of stable set partitions,the concept of its adjoint polynomials is proposed and the adjoint polynomials of several graphs are obtained.Using the adjoint polynomials,the unimodality of various graphs is demonstrated,including star graphs,complete products of star graphs,complete q-partite graphs,(n-2)-regular graphs,complete products of(n-2)-regular graphs,etc.Furthermore,the number of all possible partitions of stable sets is calculated skillfully.Finally,a generalization of the unimodal theorem is extended,and several classical examples are derived.In addition,a generalization of one form of the Newton inequalities is given,and a series of related inequalities are obtained.

关 键 词：稳定集合 分拆 伴随多项式 完全积 单峰性 

分 类 号：O157.1[理学—数学] O157.5[理学—基础数学]