Antisymmetric flows in matroids

We present a seemingly new definition of flows and flow numbers for oriented matroids and prove that the flow number ΦL and the antisymmetric flow number ΦLas of an oriented matroid are bounded with its rank. In particular we show that if O is an oriented matroid of rank r then ΦL(O) ≤ r + 2 and ΦLas(O) ≤ 3b 9 2 rc+1. Furthermore, we introduce the notion of a semiflow and show that each oriented matroid has an antisymmetric 3-NZ-semiflow.