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