On relative t-designs in polynomial association schemes

Eiichi Bannai, Etsuko Bannai, Sho Suda, Hajime Tanaka

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Motivated by the similarities between the theory of spherical t-designs and that of t-designs in Q-polynomial association schemes, we study two versions of relative t-designs, the counterparts of Euclidean t-designs for P- and/or Q-polynomial association schemes. We develop the theory based on the Terwilliger algebra, which is a noncommutative associative semisimple ℂ-algebra associated with each vertex of an association scheme. We compute explicitly the Fisher type lower bounds on the sizes of relative t-designs, assuming that certain irreducible modules behave nicely. The two versions of relative t-designs turn out to be equivalent in the case of the Hamming schemes. From this point of view, we establish a new algebraic characterization of the Hamming schemes.

Original languageEnglish
Article number#P4.47
JournalElectronic Journal of Combinatorics
Issue number4
Publication statusPublished - 2015 Dec 23


  • Fisher type inequality
  • Relative t-design
  • Terwilliger algebra

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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