New Identities for Degrees of Syzygies in Numerical Semigroups

Details New Identities for Degrees of Syzygies in Numerical Semigroups New Identities for Degrees of Syzygies in Numerical Semigroups

2009-12-28

arxiv.org/abs/0912.5192v1

Mathematics

Commutative Algebra

Primary -- 20M14, Secondary -- 11P81

Scientific paper

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.

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