New Identities for Degrees of Syzygies in Numerical Semigroups

Abstract

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.

arXiv commentPrimary -- 20M14, Secondary -- 11P81

References in corpus (1)

• Analytic Representations in the 3-dim Frobenius Problem

Cited by in corpus (2)

• On Frobenius numbers for Symmetric (not Complete Intersection) Semigroups Generated by Four Elements
• An Algebraic Proof for the Identities for Degree of Syzygies in Numerical Semigroup