Duality Relation for the Hilbert Series of Almost Symmetric Numerical Semigroups

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dc.creatorFel, Leonid G.
dc.date2008-08-17
dc.date.accessioned2026-07-07T09:57:05Z
dc.date.available2026-07-07T09:57:05Z
dc.descriptionWe derive the duality relation for the Hilbert series H(d^m;z) of almost symmetric numerical semigroup S(d^m) combining it with its dual H(d^m;z^{-1}). On this basis we establish the bijection between the multiset of degrees of the syzygy terms and the multiset of the gaps F_j, generators d_i and their linear combinations. We present the relations for the sums of the Betti numbers of even and odd indices separately. We apply the duality relation to the simple case of the almost symmetric semigroups of maximal embedding dimension, and give the necessary and efficient conditions for minimal set d^m to generate such semigroups.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0808.2297
dc.identifierhttp://arxiv.org/abs/0808.2297
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167213
dc.subjectCommutative Algebra
dc.subject20M14, 11P81
dc.titleDuality Relation for the Hilbert Series of Almost Symmetric Numerical Semigroups
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