326 research outputs found
Indispensable binomials in semigroup ideals
In this paper, we deal with the problem of uniqueness of minimal system of
binomial generators of a semigroup ideal. Concretely, we give different
necessary and/or sufficient conditions for uniqueness of such minimal system of
generators. These conditions come from the study and combinatorial description
of the so-called indispensable binomials in the semigroup ideal.Comment: 11 pages. This paper was initially presented at the II Iberian
Mathematical Meeting (http://imm2.unex.es). To appear in the Proc. Amer.
Math. So
The short resolution of a semigroup algebra
This work generalizes the short resolution given in Proc. Amer. Math. Soc.
\textbf{131}, 4, (2003), 1081--1091, to any affine semigroup. Moreover, a
characterization of Ap\'{e}ry sets is given. This characterization lets compute
Ap\'{e}ry sets of affine semigroups and the Frobenius number of a numerical
semigroup in a simple way. We also exhibit a new characterization of the
Cohen-Macaulay property for simplicial affine semigroups.Comment: 12 pages. In this new version, some proofs have been detailed, the
references on the computatation of the Frobenius number of a numerical
semigroup have been updated and some typpos have been correcte
Uniquely presented finitely generated commutative monoids
A finitely generated commutative monoid is uniquely presented if it has only
a minimal presentation. We give necessary and sufficient conditions for
finitely generated, combinatorially finite, cancellative, commutative monoids
to be uniquely presented. We use the concept of gluing to construct commutative
monoids with this property. Finally for some relevant families of numerical
semigroups we describe the elements that are uniquely presented.Comment: 13 pages, typos corrected, references update
Uniqueness of limit cycles for quadratic vector fields
Producción CientÃficaThis article deals with the study of the number of limit
cycles surrounding a critical point of a quadratic planar vector field,
which, in normal form, can be written as x
′ = a1x − y − a3x
2 + (2a2 +
a5)xy+a6y
2
, y
′ = x+a1y+a2x
2+(2a3+a4)xy−a2y
2
. In particular, we
study the semi-varieties defined in terms of the parameters a1, a2, . . . , a6
where some classical criteria for the associated Abel equation apply.
The proofs will combine classical ideas with tools from computational
algebraic geometry.Agencia Estatal de Investigación - Fondo Europeo de Desarrollo Regional (grant MTM 2011-22751)Junta de Extremadura (grant GR15055)Ministerio de EconomÃa, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant MTM2015-65764-C3-1-P
An indispensable classification of monomial curves in \mathbb{A}^4(\mathbbmss{k})
In this paper a new classification of monomial curves in
\mathbb{A}^4(\mathbbmss{k}) is given. Our classification relies on the
detection of those binomials and monomials that have to appear in every system
of binomial generators of the defining ideal of the monomial curve; these
special binomials and monomials are called indispensable in the literature.
This way to proceed has the advantage of producing a natural necessary and
sufficient condition for the definining ideal of a monomial curve in
\mathbb{A}^4(\mathbbmss{k}) to have a unique minimal system of binomial
generators. Furthermore, some other interesting results on more general classes
of binomial ideals with unique minimal system of binomial generators are
obtained.Comment: 17 pages; fixed typos, added some clarifying remarks, minor
corrections to the original version. Accepted for publication in Pacific
Journal of Mathematic
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