New Identities for Degrees of Syzygies in Numerical Semigroups

الأصل · EN

We derive a set of polynomial and quasipolynomial identities for degrees of syzygies in the Hilbert series H(dᵐ;z) of nonsymmetric numerical semigroups S(dᵐ) of arbitrary generating set of positive integers dᵐ=d₁,...,dₘ, m≥ 3. These identities were obtained by studying together the rational representation of the Hilbert series H(dᵐ;z) and the quasipolynomial representation of the Sylvester waves in the restricted partition function W(s,dᵐ). In the cases of symmetric semigroups and complete intersections these identities become more compact.