The ErdősKoRado basis for a Leonard system
Abstract
We introduce and discuss an ErdősKoRado 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 "ErdősKoRado theorems" for several classical families of $Q$polynomial distanceregular graphs, including the original 1961 theorem of Erdős, Ko, and Rado.
 Publication:

arXiv eprints
 Pub Date:
 August 2012
 DOI:
 10.48550/arXiv.1208.4050
 arXiv:
 arXiv:1208.4050
 Bibcode:
 2012arXiv1208.4050T
 Keywords:

 Mathematics  Rings and Algebras;
 05D05;
 05E30;
 33C45;
 33D45
 EPrint:
 19 pages