Mathematics – Commutative Algebra
Scientific paper
2007-03-25
Mathematics
Commutative Algebra
20 pages, 1 figure
Scientific paper
There exist two different sorts of gaps in the nonsymmetric numerical additive semigroups finitely generated by a minimal set of positive integers {d_1,...,d_m}. The h-gaps are specific only for the nonsymmetric semigroups while the g-gaps are possessed by both, symmetric and nonsymmetric semigroups. We derive the generating functions for the corresponding sets of gaps, Delta_H({\bf d}^m) and Delta_G({\bf d}^m), and prove several statements on the minimal and maximal values of the h-gaps. Detailed description of both sorts of gaps is given for three special kinds of nonsymmetric semigroups: semigroups with maximal embedding dimension, semigroups of maximal and almost maximal length, and pseudo--symmetric semigroups.
Aicardi Francesca
Fel Leonid G.
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