Annals of Combinatorics 4 (2000) 237-246


Orthogonal Matroids

Zhe-Xian Wan

Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Center for Combinatorics, Nankai University, Tianjin 300071, China
wan@it.lth.se

Received February 23, 2000

AMS Subject Classification: 05B35, 05E15

Abstract. Orthogonal matroids are meant by Coxeter matroids over the group Dn. Elementary axioms characterizing the orthogonal matroids are given. Orthogonal matroids of rank n are proved to be symplectic matroids. Representable orthogonal matroids arising from totally singular subspaces of orthogonal spaces are studied.

Keywords: orthogonal matroid, Coxeter matroid, orthogonal space, representable orthogonal matroid


References

1.  V. Borovik, I.M. Gelfand, and N. White, Symplectic matroids, J. Alg. Combin. 8 (1998) 235252.

2.  D. Gale, Optimal assignments in an ordered set: An application of matriod theory, J. Combin. Theory 4 (1968) 10731082.

3.  Loo-Keng Hua and Zhe-Xian Wan, Classical Groups, Shanghai Science and Technology Press, Shanghai, 1963 (in Chinese).

4.  J. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, 1990.

5.  N. White, The Coxeter matroids of Gelfand et al., In: Matriod Theory, Contempory Mathematics, Vol. 197, American Mathematical Society, 1996, pp. 401409.


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