The Erdős-Ko-Rado basis for a Leonard system
Abstract
We introduce and discuss an Erdős-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 "Erdős-Ko-Rado theorems" for several classical families of $Q$-polynomial distance-regular graphs, including the original 1961 theorem of Erdős, Ko, and Rado.
- Publication:
-
arXiv e-prints
- 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
- E-Print:
- 19 pages