Transversals for association schemes

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Generalizing a well-known group-theoretical notion we define transversals for (association) schemes. Two results on transversals of schemes are offered. Firstly, we show that a closed subset in a scheme possesses a factor scheme if it possesses a transversal. Secondly, we characterize the Coxeter schemes in terms of transversals. (Coxeter schemes are exactly those schemes which can be identified with the buildings in the sense of Tits). The second result may be viewed as a"thick version"of the characterization of Coxeter groups by the existence of"minimal coset representatives". On the other hand, the characterizing conditions given in this result are similar to the well-known"gate property"defined for chamber systems having a Coxeter matrix as type. Thus, our second main result may be viewed as a unified treatment of these two results.

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 52(2), 465-482, 2000-04 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10004480373
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    5374873
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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