Symmetries on almost symmetric numerical semigroups

By Hirokatsu Nari. 2011

61 citations recorded by the source corpus.

The notion of an almost symmetric numerical semigroup was given by V. Barucci and R. Fröberg 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 H1 or H2 is not symmetric, then the gluing of H1 and H2 is not almost symmetric.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c19f4a3088d1338128163aec40e5e177d9445550

How researchers see this paper

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In Algebra and Number Theory

1. Takayuki Hibi
2. Jürgen Herzog
3. Dumitru I. Stamate
4. Asia Rauf
5. Adam Van Tuyl
6. Huy Tài Hà
7. Susan Morey
8. Giancarlo Rinaldo

In Computational Theory and Mathematics

1. Takayuki Hibi
2. Jürgen Herzog
3. Dumitru I. Stamate
4. Asia Rauf
5. Huy Tài Hà
6. Susan Morey
7. Adam Van Tuyl
8. Giancarlo Rinaldo

In Geometry and Topology

1. Jürgen Herzog
2. Takayuki Hibi
3. Dumitru I. Stamate
4. Huy Tài Hà
5. Susan Morey
6. Ngô Viêt Trung
7. Rafael H. Villarreal
8. Adam Van Tuyl

Citations in the corpus

• The trace of the canonical module (2016, background): “z [24] showed that K[H] is Gorenstein if and only if His symmetric, i.e. for all x∈ Zeither x∈ H, or F(H)−x∈ H. Let PF(H) = {f 1,...,fτ−1,F(H)}, with fi<fi+1 for 1 ≤ i<τ− 2. It is known by Nari [27] that K[H] is almost Gorenstein, if and only if (10) fi+fτ−i= F(H) for i= 1,...,⌊τ/2⌋. The semig”