The Erdos-Ko-Rado basis for a Leonard system

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Abstract

We introduce and discuss an Erdos-Ko-Rado basis of the vector space underlying a Leonard system Φ= ( A;A*; {Ei}d i=0; {E* i}d i=0 ) that satisfies a mild condition on the eigenvalues of A and A*. We de- scribe 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 \Erdos-Ko- Rado theorems" for several classical families of Q-polynomial distance- regular graphs, including the original 1961 theorem of Erdos, Ko, and Rado.

Original languageEnglish
Pages (from-to)41-59
Number of pages19
JournalContributions to Discrete Mathematics
Volume8
Issue number2
Publication statusPublished - 2013

Keywords

  • Distance-regular graph
  • Erdos-Ko-Rado theorem
  • Leonard system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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