The Erdős-Ko-Rado basis for a Leonard system

Contributions to Discrete Mathematics

Hajime Tanaka¹ 

[1] Division of Mathematics, Graduate School of Information Sciences, Tohoku University

关键词: Leonard system;    ErdH{o}s-Ko-Rado theorem;    Distance-regular graph;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

We introduce and discuss an Erd\H{o}s-Ko-Rado basis for the underlying vector space of a Leonard system $\Phi = (A; A^*; \{E_i\}_{i=0}^d ; \{E_i^* \}_{i=0}^d)$ 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 "Erd\H{o}s-Ko-Rado theorems" for several classical families of $Q$-polynomial distance-regular graphs, including the original 1961 theorem of Erd\H{o}s, Ko, and Rado.

【 授权许可】

Unknown