scholarly journals On minimal presentations of shifted affine semigroups with few generators

2021 ◽  
Vol 14 (4) ◽  
pp. 617-630
Author(s):  
Christopher O’Neill ◽  
Isabel White
Keyword(s):  
Affine Semigroups ◽  
Minimal Presentations

scholarly journals Isolated factorizations and their applications in simplicial affine semigroups

2019 ◽  
Vol 19 (05) ◽  
pp. 2050082 ◽  
Author(s):  
Pedro A. García-Sánchez ◽  
Andrés Herrera-Poyatos
Keyword(s):  
Complete Intersection ◽  
Minimal Element ◽  
Numerical Semigroups ◽  
Commutative Monoid ◽  
Generalize Formula ◽  
Affine Semigroups ◽  
Minimal Presentations ◽  
Minimal Generators

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups. We also generalize [Formula: see text]-rectangular numerical semigroups to the context of simplicial affine semigroups and study their isolated factorizations. As a consequence of our results, we characterize those complete intersection simplicial affine semigroups with only one Betti minimal element in several ways. Moreover, we define Betti sorted and Betti divisible simplicial affine semigroups and characterize them in terms of gluings and their minimal presentations. Finally, we determine all the Betti divisible numerical semigroups, which turn out to be those numerical semigroups that are free for any arrangement of their minimal generators.

On Cohen-Macaulay and Gorenstein simplicial affine semigroups

1998 ◽  
Vol 41 (3) ◽  
pp. 517-537 ◽  
Author(s):  
J. C. Rosales ◽  
Pedro A. García-Sánchez
Keyword(s):  
Semigroup Ring ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Minimal Presentations

We give arithmetic characterizations which allow us to determine algorithmically when the semigroup ring associated to a simplicial affine semigroup is Cohen-Macaulay and/or Gorenstein. These characterizations are then used to provide information about presentations of this kind of semigroup and, in particular, to obtain bounds for the cardinality of their minimal presentations. Finally, we show that these bounds are reached for semigroups with maximal codimension.

scholarly journals Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

2021 ◽  
Vol 102 (2) ◽  
pp. 340-356
Author(s):  
Tristram Bogart ◽  
John Goodrick ◽  
Kevin Woods
Keyword(s):  
Periodic Behavior ◽  
Presburger Arithmetic ◽  
Affine Semigroups

scholarly journals Unital affine semigroups

2013 ◽  
Vol 439 (7) ◽  
pp. 2106-2113 ◽  
Author(s):  
David W. Kribs ◽  
Jeremy Levick ◽  
Rajesh Pereira
Keyword(s):  
Affine Semigroups

Minimal Presentations

2016 ◽  
pp. 69-83
Author(s):  
Abdallah Assi ◽  
Pedro A. García-Sánchez
Keyword(s):  
Minimal Presentations

scholarly journals On the computation of the Apéry set of numerical monoids and affine semigroups

2014 ◽  
Vol 91 (1) ◽  
pp. 139-158 ◽  
Author(s):  
Guadalupe Márquez-Campos ◽  
Ignacio Ojeda ◽  
José M. Tornero
Keyword(s):  
Apéry Set ◽  
Affine Semigroups
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