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April, 2000 Transversals for association schemes
Paul-Hermann ZIESCHANG
J. Math. Soc. Japan 52(2): 465-482 (April, 2000). DOI: 10.2969/jmsj/05220465


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.


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Paul-Hermann ZIESCHANG. "Transversals for association schemes." J. Math. Soc. Japan 52 (2) 465 - 482, April, 2000.


Published: April, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0958.05142
MathSciNet: MR1742793
Digital Object Identifier: 10.2969/jmsj/05220465

Primary: 05E30
Secondary: 51E24

Keywords: association schemes , buildings , transversals of association schemes

Rights: Copyright © 2000 Mathematical Society of Japan


Vol.52 • No. 2 • April, 2000
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