Contributions to Discrete Mathematics | |
The Erdős-Ko-Rado basis for a Leonard system | |
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
【 预 览 】
Files | Size | Format | View |
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RO201911300286702ZK.pdf | 378KB | download |