Two Conclusions About Sign Idempotent Sign Patterns

Sign pattern is a hot topic in combinatorial mathematics. It has very important applicationin the areas of economics, biology and chemistry. We research the properties about full signidempotent sign patterns and get the number and the upper bound of negative entries in signidempotent sign patterns. according the existing results in sign patterns and the mathematicalmethods involved.In chapter one, the history of development and research status about sign patterns arechiefly introduced. The basic concepts, major achievements and the main conclusions of thisthesis are provided.In chapter two, the properties of full sign idempotent sign patterns are discussed.In chapter three, we get the upper bound of negative entries in irreducible sign idempotentsign patterns by another method. The upper bound about negative entries in symmetric andreducible sign idempotent sign patterns is better than the bound in the reference[1].Meanwhile we gain the upper bound of negative entries in reducible sign idempotent signpatterns when mr (A)2.