Séminaire Lotharingien de Combinatoire, B06k (1982), 1 p.
[Formerly: Publ. I.R.M.A. Strasbourg, 1982, 191/S-05, p.
98.]
Achim Bachem
On Polars of Face Lattices of Oriented Matroids
Abstract.
The positive cocircuits of oriented matroids can be used to define two
classes of face lattices of oriented matroids.
(Edmonds-Mandel and Las-Vergnas lattices), each of which is polar to
the other. Both lattices generalize polytopal face lattices, but
neither class of lattices is contained in the other. This implies
that matroid analogs of the results of Weyl"and Minkowski do not hold.
In this paper we characterize those oriented matroids having a polar.
We also give some results on extentions and adjoinfcs of oriented
matroids and discuss results on oriented matroid inner products.
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