Abstract
We have seen how matroids and semimodular lattices are intimately related to the symmetric group. Now we replace the symmetric group by another Coxeter group, namely, BC n the hyperoctahedral group. The resulting structures are called symplectic matroids, and they are in some sense rather general Coxeter matroids, as they include ordinary matroids and a third type, orthogonal matroids, as special cases. This will also prepare us to tackle Coxeter matroids in full generality in the later chapters.
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© 2003 Birkhäuser Boston
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Borovik, A.V., Gelfand, I.M., White, N. (2003). Symplectic Matroids. In: Coxeter Matroids. Progress in Mathematics, vol 216. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2066-4_3
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DOI: https://doi.org/10.1007/978-1-4612-2066-4_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7400-1
Online ISBN: 978-1-4612-2066-4
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