Symmetric polynomials associated with numerical semigroups

We study a new kind of symmetric polynomials P_n(x_1,...,x_m) degree n in m real variables, which have arisen the theory numerical semigroups. establish their basic properties and find representation through power sums E_k=\sum_{j=1}^m x_j^k. observe visual similarity between normalized P_n(x_1,...,x_m)/\chi_m, where \chi_m=\prod_{j=1}^m x_j, polynomial part partition function W(s,{d_1,...,d_m}), gives number partitions s\ge 0 into positive integers d_j, put forward conjecture about relationship.