Leonard系统的Erdens-Ko-Rado基
The Erdős-Ko-Rado basis for a Leonard system
摘要：
我们引入并讨论了Leonard系统$Φ= (A; A^*; \{E_i\}_{i=0}^d ; \{E_i^* \}_{i=0}^d)$的底层向量空间的Erdens-Ko-Rado基，该系统满足关于$A$和$A^*$的特征值的一个温和条件.我们描述的转移阵/从其他已知的基础，以及矩阵表示$A$和$A^*$相对于新的基础。我们还讨论了如何这些结果可以被看作是一个推广的线性规划方法中使用的“Erdens-Ko-Rado定理”的几个经典的家庭的$Q$ -多项式距离正则图，包括原来的1961年的Erdens-Ko定理，和Rado的证明。
英文摘要：
We introduce and discuss an Erdős-Ko-Rado basis for the underlying vector space of a Leonard system $Φ= (A; A^*; \{E_i\}_{i=0}^d ; \{E_i^* \}_{i=0}^d)$ that satisfies a mild condition on the eigenvalues of $A$ and $A^*$. We describe the transition matrices to/from other known bases, as well as the matrices representing $A$ and $A^*$ with respect to the new basis. We also discuss how these results can be viewed as a generalization of the linear programming method used previously in the proofs of the "Erdős-Ko-Rado theorems" for several classical families of $Q$-polynomial distance-regular graphs, including the original 1961 theorem of Erdős, Ko, and Rado.
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。
