  We derive a set of polynomial and quasipolynomial identities for degrees of
syzygies in the Hilbert series H(d^m;z) of nonsymmetric numerical semigroups
S(d^m) of arbitrary generating set of positive integers d^m={d_1,...,d_m},
m\geq 3. These identities were obtained by studying together the rational
representation of the Hilbert series H(d^m;z) and the quasipolynomial
representation of the Sylvester waves in the restricted partition function
W(s,d^m). In the cases of symmetric semigroups and complete intersections these
identities become more compact.
