Journal of Algebraic Combinatorics

, Volume 25, Issue 4, pp 399–415 | Cite as

Imprimitive cometric association schemes: Constructions and analysis

  • William J. MartinEmail author
  • Mikhail Muzychuk
  • Jason Williford


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.


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


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • William J. Martin
    • 1
    Email author
  • Mikhail Muzychuk
    • 2
  • Jason Williford
    • 3
  1. 1.Department of Mathematical Sciences and Department of Computer ScienceWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Department of Computer Science and MathematicsNetanya Academic CollegeNetanyaIsrael
  3. 3.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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