The switching game on unions of oriented matroids

In 1986, Hamidoune and Las Vergnas [3] introduced an oriented matroid version of the so-called Shannon’s switching game. They conjectured that the classification of the directed switching game on oriented matroids is identical to the classification of the non-oriented version. In this note, we support this conjecture by showing its validity for an infinite class of oriented matroids obtained as unions of rank-1 and/or rank-2 uniform oriented matroids.