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arXiv · 1208.4050

The Erd\H{o}s-Ko-Rado basis for a Leonard system

Hajime Tanaka
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Abstract

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.

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Hajime Tanaka. 2012-08-20. The Erd\H{o}s-Ko-Rado basis for a Leonard system. https://doi.org/10.11575/cdm.v8i2.62172

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