论文标题
平衡邻居多项式的存在
The existence of balanced neighborly polynomials
论文作者
论文摘要
受到平衡邻居领域的定义的启发，我们定义了平衡的邻居多项式，并研究了这些多项式的存在。本文的目的是在任何$ k \ neq 2 $上构建$ $ k $ type $（k，k，k，k）$的平衡邻居多项式，并表明当$（2,2,2,2,2）$的均衡邻邻邻域$（2,2,2,2）$都存在，并且仅当$ {\ rm char}（k char}（k）（k）（k）（k）（k）（k）（k）（k）（k）（k）（k）此外，我们还讨论了平衡的邻居多项式与平衡的邻居简单球之间的关系。
Inspired by the definition of balanced neighborly spheres, we define balanced neighborly polynomials and study the existence of these polynomials. The goal of this article is to construct balanced neighborly polynomials of type $(k,k,k,k)$ over any field $K$ for all $k \neq 2$, and show that a balanced neighborly polynomial of type $(2,2,2,2)$ exists if and only if ${\rm char}(K) \neq 2$. Besides, we also discuss a relation between balanced neighborly polynomials and balanced neighborly simplicial spheres.
