Antisymmetric flows in matroids

Abstract

We present a seemingly new definition of flows and flow numbers in oriented matroids and prove that the flow number and the antisymmetric flow number in an oriented matroid are bounded with its rank. In particular we show that any orientable matroid O has an antisymmetric 3 ⌊ 9 2 ⌋ r ( E ) + 1 -flow. Furthermore we introduce the notion of a semiflow and show that each oriented matroid has a 3-NZ-semiflow which is even an antisymmetric 3-NZ-semiflow.