Abstract: Firstly, we gave the definition of the generalized general position arrangement, and studied the relationships among the general position arrangements, generalized general position arrangements and generic arrangements. Secondly, by establishing the relationships between arrangements and the simple graphs, we gave the necessary and sufficient   condition for linear independence of the subarrangements of generic threshold arrangements and the characteristic polynomials of the subarrangements of generic threshold arrangements.

Key words: generic arrangement, general position, generic threshold arrangement, characteristic polynomial