Properties and Applications of Permutation and Combinatorial Functions

This paper introduces permutation and combination functions.It extends the conception of permutation and combinatorial numbers,obtains some properties of permutation and combination functions,and gets the relationship between generalized and ordinary combinatorial(permutation) numbers.Some new combinatorial identities are also obtained according to the generalized binomials,we derives the linear expression of about permutation and combination functions,the recurrence relation of the expressions' coefficients and the new coefficients formula,as well as four expression of sum of equal powers.