Symmetries on almost symmetric numerical semigroups
TLDR
Barucci and Froberg as discussed by the authors characterized almost symmetric numerical semigroups by symmetry of pseudo-Frobenius numbers and gave a criterion for H� ∗ (the dual of M) to be an almost-symmetric semigroup.Abstract:
The notion of an almost symmetric numerical semigroup was given by V. Barucci and R. Froberg in J. Algebra, 188, 418–442 (1997). We characterize almost symmetric numerical semigroups by symmetry of pseudo-Frobenius numbers. We give a criterion for H
∗ (the dual of M) to be an almost symmetric numerical semigroup. Using these results we give a formula for the multiplicity of an opened modular numerical semigroup. Finally, we show that if H
1 or H
2 is not symmetric, then the gluing of H
1 and H
2 is not almost symmetric.read more
Citations
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One-dimensional Gorenstein local rings with decreasing Hilbert function
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References
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TL;DR: In this paper, the authors cover maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, with a focus on the maximality property of one dimensional local domains.
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