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Weak metric and weak cometric schemes

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The notion of weak metric and weak cometric schemes are introduced as a generalization of metric and cometric schemes. They are given as the wreath product of a finite number of symmetric association schemes satisfying certain equivalent conditions which are analogous to the ones for metric or cometric schemes. We characterize those schemes and determine some of their parameters.

Abstract

The notion of weak metric and weak cometric schemes are introduced as a generalization of metric and cometric schemes. They are given as the wreath product of a finite number of symmetric association schemes satisfying certain equivalent conditions which are analogous to the ones for metric or cometric schemes. We characterize those schemes and determine some of their parameters.

참고문헌 (9)

  1. S. Bang, "On generalized semidirect product of association schemes", Discrete Math., 303(1), pp.5~16 (2005)
  2. E. Bannai, "Algebraic combinatorics", pp.1984, The Ben- jamin
  3. A. E. Brouwer, "Distance-Regular Graphs, Ergebnisse der Mathematik und ihrer Grenzgebiete (3)", Springer-Verlag, 18 (1989)
  4. R. A. Brualdi, "Codes with a poset metric", Discrete Math, 147(1), pp.57~72 (1995)
  5. D. S. Kim, "MacWilliams-type identities for fragment and sphere enumerators", European J. Combin., 28(1), pp.273~302 (2007)
  6. D. S. Kim, "Dual MacWilliams pair, IEEE Trans", Inform. Theory, 5(8), pp.2901~2905 (2005)
  7. H. K. Kim, "A classification of posets admitting the MacWilliams identity", IEEE Trans. Inform. Theory, 51(4), pp.1424~1431 (2005)
  8. H. K. Kim, "Association schemes for poset metrics and MacWilliams duality", to submit, ~
  9. S. Y. Song, "Fusion relation in products of association schemes", Graphs Combin, 18(3), pp.655~665 (2002)

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