论文标题
狄拉克（Goodman-goodman-Pollack）猜想
The Dirac--Goodman--Pollack Conjecture
论文作者
论文摘要
在有关允许序列的一篇开创性文章中，古德曼（Goodman）和波拉克（Pollack）为离散几何学的三个问题提供了组合概括，其中之一就是狄拉克（Dirac）的猜想。根据这一猜想，飞机上的任何一组$ n $ noncolrinear点都有一个点事件，至少由$ c n $连接线确定。允许排列序列的概念为分析这些问题提供了自然的组合设置。在这种形式主义中，猜想的概括如下：\ emph {任何非平凡的允许$ n $ - 序列$σ$具有局部序列$λ_i$，其半径至少为$ c n $。}在这里确认了构想，并在此确认具有混凝土$ c = 1/845 $。讨论了几个相关问题。
In one of their seminal articles on allowable sequences, Goodman and Pollack gave combinatorial generalizations for three problems in discrete geometry, one of which being the Dirac conjecture. According to this conjecture, any set of $n$ noncollinear points in the plane has a point incident to at least $c n$ connecting lines determined by the set. The notion of allowable sequences of permutations provides a natural combinatorial setting for analyzing these problems. Within this formalism, the conjectured generalization reads as follows: \emph{Any nontrivial allowable $n$-sequence $Σ$ has a local sequence $Λ_i$ whose half-period is at least $c n$.} The conjecture is confirmed here with a concrete bound $c=1/845$. Several related problems are discussed.
