Research on Algebraic Solutions of the Covering Graphics Problem with the Odd-even Features

摘要

For the covering graphics problem with the odd-even features, it is often solved by parity method, which is simple and ingenious. However, this method lacks of logical derivation and proof. Moreover, when the scale of the graphics problem is large, it's hard to use this method. By establishing a coordinate system and corresponding coordinate transform principles, the geometrical problem can be transformed to solve the integer solutions of an algebraic equation. It can not only prove the validity of parity checking, but also explain the theory of parity checking. Finally, the tiling problem is generated and the results of generalized case are given.