Planar Orlik-solomon Algebra And ¦Õ <sub> 3 </ Sub> Variable Calculation

In chapter one, we introduce hyperplane arrangements includingdefinitions, examples, and related materials, e.g., the partial ordered set ofthe intersections, its Mobius function and Poincare polynomial, which arecombinatorial invariants of the arrangement. In chapter two we introduce theOrlik-Solomon algebra, discuss the Combinatorial and Topological propertiesof Orlik-Solomon algebra. In the end of chapter two we give an algorithm forcomputing Orlik-Solomon algebra, and the specific Matlab program. Thisprogram was used to compute the Orlik-Solomon algebra of arrangementsassociated with signed complete graphic arrangements on n vertices with n＜8,meanwhile we find some particular examples. In chapter three we describedan algorithm aboutφ₃, which is an invariant of hyperplane arrangement, andrealize the program on computer. As an application, we found and proved thatφ₃=2m on wheel graphic with m+1 vertices.