THE STUDY TO THE PRODUCT SUMMATION OF ORDERED PARTITIONS

By studying the j-degree product summation k ordered partitions of n and the homogeneous(r-degree) product summation k ordered partitions of n,the explicit result of the jdegree product summation k ordered partitions of n and some special homogeneous(r-)degree product summation k ordered partitions of n are obtained by induction.Moreover,the relation between the j-degree product summation k ordered partitions of n and the Fibonacci numbers,the Lucas numbers is discussed.A new explanation to the Fibonacci numbers is obtained.