Imprimitive cometric association schemes: Constructions and analysis

William J. Martin, Mikhail Muzychuk, Jason Williford

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Dualizing the "extended bipartite double" construction for distance-regular graphs, we construct a new family of cometric (or Q-polynomial) association schemes with four associate classes based on linked systems of symmetric designs. The analysis of these new schemes naturally leads to structural questions concerning imprimitive cometric association schemes, some of which we answer with others being left as open problems. In particular, we prove that any Q-antipodal association scheme is dismantlable: the configuration induced on any subset of the equivalence classes in the Q-antipodal imprimitivity system is again a cometric association scheme. Further examples are explored.

Original languageEnglish
Pages (from-to)399-415
Number of pages17
JournalJournal of Algebraic Combinatorics
Issue number4
StatePublished - 1 Jun 2007
Externally publishedYes


  • Association scheme
  • Cometric
  • Imprimitive
  • Linked system of symmetric designs
  • Q-polynomial
  • Spherical design

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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