Abstract
The purpose of this note is to give an example of a rank-4 matroid which not only shows that Levi's intersection property is not a sufficient condition for the existence of an adjoint but also seems to have an interesting structure of the lattice of flats.
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References
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Bachem, A., Wanka, A. Matroids without adjoint. Geom Dedicata 29, 311–315 (1989). https://doi.org/10.1007/BF00572447
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DOI: https://doi.org/10.1007/BF00572447