Imprimitive Q-polynomial Association Schemes

  • Authors:

  • Hiroshi Suzuki

  • Affiliations:

  • Department of Mathematics, International Christian University, 10-2, Osawa 3-chome, Mitaka-shi Tokyo 181, Japan. E-mail: hsuzuki@icu.ac.jp

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 1998

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Abstract

It is well known that imprimitive P-polynomial association schemes\cX = (X,\{R_i\}_{0\leq i\leq d}) with k_1 2 are either bipartiteor antipodal, i.e., intersection numbers satisfy either a_i = 0 for alli, or b_i = c_{d-i} for all i\ne [d/2]. In this paper, we show thatimprimitive Q-polynomial association schemes \cX = (X,\{R_i\}_{0\leqi\leq d}) with d6 and k^*_12 are either dual bipartite or dualantipodal, i.e., dual intersection numbers satisfy either a^*_i =0 forall i, or b^*_i = c^*_{d-i} for all i\ne[d/2].