论文标题
球形建筑物中的Erdős-Ko-Rado套装的代数方法
An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings
论文作者
论文摘要
在本文中，球形建筑物中的相反性用于定义射影和极性空间中标志的EKR问题。开发了建筑理论和Iwahori-Hecke代数的新颖应用，以证明EKR量的旗帜上的急剧上限。在此框架中，我们可以在投影和极性空间中对EKR问题的先前上限进行谴责和概括。边界是通过限制在对立图的Delsarte-Hoffman Coclique获得的。其特征值的计算是由于Andries Brouwer的较早工作以及明确的算法。对于经典的几何形状，该算法的执行归结为基本组合物。简要讨论了与建筑理论的联系，伊瓦霍里 - 赫克代数，古典群体和图几何形状。到最后，整个过程中都提出了几个开放问题。
In this paper, oppositeness in spherical buildings is used to define an EKR-problem for flags in projective and polar spaces. A novel application of the theory of buildings and Iwahori-Hecke algebras is developed to prove sharp upper bounds for EKR-sets of flags. In this framework, we can reprove and generalize previous upper bounds for EKR-problems in projective and polar spaces. The bounds are obtained by the application of the Delsarte-Hoffman coclique bound to the opposition graph. The computation of its eigenvalues is due to earlier work by Andries Brouwer and an explicit algorithm is worked out. For the classical geometries, the execution of this algorithm boils down to elementary combinatorics. Connections to building theory, Iwahori-Hecke algebras, classical groups and diagram geometries are briefly discussed. Several open problems are posed throughout and at the end.
