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doi.org/10.1080/07468342.2021.1909953Luck is a dividend of sweat. The more you sweat, the luckier you get.- Ray Kroc [21]In [15], the authors examined in detail the Chicken McNugget Monoid (denoted...

In this paper, we study a family of binomial ideals defining monomial curves in the n-dimensional affine space determined by n hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}}$ in $\Bbbk [x_1, \ldots , x_n]$ with $u_{ii} = 0, \ i\in \{ 1, \ldots , n\}$ . We prove that the monomial curves in that family are set-theoretic complete intersections. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Frobenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.

Le dialogue instaure avec Aaron Cicourel lors de la preparation de la recherche sur laquelle s’appuie cet article a marque le rapport de son auteur a l’ethnographie urbaine et au suivi des interactions. L’etude des violences liees a l’usage des espaces publics a Caracas et a la fragilite du lien civil a servi a esquisser une ecologie de l’ordre public. Attentive a la perception des troubles et aux interdependances environnementales, cette ecologie s’interesse egalement aux grammaires de l’action et aux arriere-plans cognitifs participant a la resolution quotidienne des problemes. Garder un œil rive sur l’emboitement problematique micro-macro dans des contextes imbibes d’implicites est une precaution utile lorsque l’on enquete sur des activites reputees dangereuses. Suivre la trame sensible et les hyperboles interpretatives fait apparaitre la versatilite semantique du prisme de l’insecurite. Comment peuvent etre deceles sociologiquement differents troubles pour les memes violences quand le cadre de pertinence n’assurera pas d’expertise juridique, ni de suivi judiciaire ? La juste mesure du social a Caracas, dans ses epreuves civiles et urbaines, est ainsi mise en perspective.

We give an algorithm to determine whether Wilf’s conjecture holds for all numerical semigroups with a given multiplicity [Formula: see text], and use it to prove Wilf’s conjecture holds whenever [Formula: see text]. Our algorithm utilizes techniques from polyhedral geometry, and includes a parallelizable algorithm for enumerating the faces of any polyhedral cone up to orbits of an automorphism group. We also introduce a new method of verifying Wilf’s conjecture via a combinatorially flavored game played on the elements of a certain finite poset.

We prove a general structure theorem by which an inside factorial monoid can be uniquely decomposed into a factorial monoid and the related Apery set. The structure of the latter is analyzed subsequently. As an example, we study the Cale monoid of nonnegative solutions of equations of the form a 1 x 1 + ⋯ + a r − 1 x r − 1 = a r x r for positive integers a 1 , … , a r . In this case, the monoid is isomorphic to a simplicial full affine semigroup, and the factorial monoid of the decomposition is generated by extremal rays. For the special case r = 3 , we discuss the relationship to a kind of unique representation as studied by Elliott for a r ≤ 10 .

We study the cyclotomic exponent sequence of a numerical semigroup $S,$ and we compute its values at the gaps of $S,$ the elements of $S$ with unique representations in terms of minimal generators, and the Betti elements $b\in S$ for which the set $\{a \in \operatorname{Betti}(S) : a \le_{S}b\}$ is totally ordered with respect to $\le_S$ (we write $a \le_S b$ whenever $a - b \in S,$ with $a,b\in S$). This allows us to characterize certain semigroup families, such as Betti-sorted or Betti-divisible numerical semigroups, as well as numerical semigroups with a unique Betti element, in terms of their cyclotomic exponent sequences. Our results also apply to cyclotomic numerical semigroups, which are numerical semigroups with a finitely supported cyclotomic exponent sequence. We show that cyclotomic numerical semigroups with certain cyclotomic exponent sequences are complete intersections, thereby making progress towards proving the conjecture of Ciolan, Garc\'ia-S\'anchez and Moree (2016) stating that $S$ is cyclotomic if and only if it is a complete intersection., Comment: 25 pages

In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers. In this paper we develop for a wide class of non-factorial monoids a concept of stratification for atoms which allows to represent each element as a linear combination of atoms where the coefficients are uniquely determined when restricted in a particular way. This wide class includes inside factorial monoids and in particular simplicial affine semigroups. In the latter case the question of uniqueness is related to a problem studied by E. B. Elliott in a paper from 1903. For the monoid of all nonnegative solutions of a certain linear Diophantine equation in three variables, Elliott considers "simple sets of solutions" (atoms of the monoid) and looks for a method that gives "every set once only". We show that for simplicial affine semigroups in two dimensions a stratification is always possible, which answers to Elliott's problem also for the cases he left open. The results in this paper on the stratification of atoms for monoids in general may be seen also as an answer to a "generalized Elliott problem".

Let K be a field and denote by K[t], the polynomial ring with coefficients in K. Set A = K[f1,. .. , fs], with f1,. .. , fs ∈ K[t]. We give a procedure to calculate the monoid of degrees of the K algebra M = F1A + · · · + FrA with F1,. .. , Fr ∈ K[t]. We show some applications to the problem of the classification of plane polynomial curves (that is, plane algebraic curves parametrized by polynomials) with respect to some oh their invariants, using the module of Kahler differentials.

Made available in DSpace on 2018-11-26T17:51:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-01-01 Ministry of Economy and Competitiveness Seneca Foundation from Murcia Region Foundation for Research Support of Sao Paulo State Chroothece has been reported from a range of freshwater environments, including streams, shallow ponds, trickling water on cliffs and moist soils, mostly in Europe and North America. The identification of genera and species by morphology is difficult because of overlaps in critical characters. To help clarify diversity within the genus, samples from Spain and from other regions (UK and Guam, western Pacific) were compared. Ecological and morphological data from field and cultured material were correlated with molecular data (rbcL gene sequences) that differentiate two new species: Chroothece thermalis I. Chapuis, P. Sanchez, M. Aboal & O. Necchi Jr., sp. nov. in a thermal spring and Chroothece lobata M. Aboal, B. A. Whitton, I. Chapuis, P. Sanchez & O. Necchi Jr., sp. nov. in a semi-arid stream. The results suggest recognition of four species, C. thermalis, C. lobata, C. richteriana Hansgirg and C. rupestris Hansgirg, from Spain. Morphology and ecology are useful to help distinguish these species, but the genus needs further study for possible cryptic diversity. Fac Biol, Dept Plant Biol, Lab Algol, Espinardo Campus, E-30100 Murcia, Spain Granada Univ, Bot Dept, E-18071 Granada, Spain Univ Granada Herbarium, C Rector Lopez Argueta 8, Granada 18071, Spain Univ Melbourne, Sch BioSci 2, Parkville, Vic 3010, Australia Univ Durham, Dept Biosci, Durham DH1 3LE, England Sao Paulo State Univ, Zool & Bot Dept, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Sao Paulo State Univ, Zool & Bot Dept, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Ministry of Economy and Competitiveness: CGL2009-09563 Seneca Foundation from Murcia Region: 0572/PI/07 Foundation for Research Support of Sao Paulo State: 2012/12016-6

In this manuscript we show that the second Feng–Rao number of any telescopic numerical semigroup agrees with the multiplicity of the semigroup. To achieve this result we first study the behavior of Apery sets under gluings of numerical semigroups. These results provide a bound for the second Hamming weight of one-point Algebraic Geometry codes, which improves upon other estimates such as the Griesmer Order Bound.

This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three numerical semigroup. Also, as a consequence of these resutls, the sets that can be realized as Delta sets of numerical semigroups of embedding dimension three are fully characterized.

Let f 1 , ź , f s be formal power series (respectively polynomials) in the variable x. We study the semigroup of orders of the formal series in the algebra K ź f 1 , ź , f s ź ź K ź x ź (respectively the semigroup of degrees of polynomials in K f 1 , ź , f s ź K x ). We give procedures to compute these semigroups and several applications. We prove in particular that the space curve parametrized by f 1 , ź , f s has a flat deformation into a monomial curve.

This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three numerical semigroup. Also, as a consequence of these results, the sets that can be realized as Delta sets of numerical semigroups of embedding dimension three are fully characterized.

We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. These semigroups are affine semigroups, which in particular implies that they are finitely generated. For a given finite set of elements in $\mathbb{N}^d$ we show how to deduce if the monoid spanned by this set is a generalized numerical semigroup and, if so, we calculate its set of gaps. Also, given a finite set of elements in $\mathbb{N}^d$ we can determine if it is the set of gaps of a generalized numerical semigroup and, if so, compute the minimal generators of this monoid. We provide a new algorithm to compute the set of all generalized numerical semigroups with a prescribed genus (the cardinality of their sets of gaps). It was used to compute the number of such semigroups, and its implementation allowed us to compute (for various dimensions) the number of numerical semigroups for genus that had not been attained before., 17 pages, 3 tables, some refinement and new observations made

We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements, and a description of its convex hull. We also study the associated monoid ring, proving that it is normal, and thus Cohen-Macaulay. We determine its Cohen-Macaulay type, characterize the Gorenstein property, and provide a Gr\"obner basis of the defining ideal. Then we apply these results to the monoid of quasi-arithmetic multiplicities on a uniform matroid. Finally we state some conjectures on the number of irreducibles for the monoid of multiplicities on an arbitrary matroid., Comment: Final version, to appear on Journal of Algebra

Let f be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated ?-sequence, and consequently its value semigroup. For a ?-sequence we present a procedure to construct all curves having this associated sequence. Also for a fixed genus (equivalently Frobenius number) we construct all ?-sequences generating numerical semigroups with this given genus.We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.

The package numericalsgps performs computations with and for numerical semigroups. Recently also affine semigroups are admitted as objects for calculations. This manuscript is a survey of what the package does, and at the same time of the trending topics on numerical semigroups., Comment: 12 pages

Producción Científica, We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, we compute the second Feng-Rao number, and provide some examples and comparisons with previous results on this topic. These calculations rely on Apéry sets, and thus several results concerning Apéry sets of Arf semigroups are presented., Ministerio de Economía, Industria y Competitividad; y Fondo Europeo de Desarrollo Regional FEDER( Projects MTM2014-55367-P / MTM2015-65764-C3-1-P), Junta de Andalucía (Grant FQM-343), Fundação para a Ciência e a Tecnologia (Project UID/MAT/00297/2013)

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 $\alpha$-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., Comment: Version 1 and the published version contain an error in the proof of c) implies a) in Theorem 7.12. This implication has been removed in this new version, and a counter example provided by I. Garc\'ia-Marco and C. Tatakis has been included (along with a reference to the paper where they give this counterexample)

Value semigroups of non-irreducible singular algebraic curves and their fractional ideals are submonoids of [Formula: see text] that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements. Monoids of [Formula: see text] fulfilling these three conditions are known in the literature as good semigroups and there are examples of good semigroups that are not realizable as the value semigroup of an algebraic curve. In this paper, we consider good semigroups independently from their algebraic counterpart, in a purely combinatorial setting. We define the concept of good system of generators, and we show that minimal good systems of generators are unique. Moreover, we give a constructive way to compute the canonical ideal and the Arf closure of a good subsemigroup when [Formula: see text].

The second Feng-Rao number of every inductive numerical semigroup is explicitly computed. This number determines the asymptotical behavior of the order bound for the second Hamming weight of one-point algebraic geometry codes. In particular, this result is applied for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, some properties of inductive numerical semigroups are studied, the involved Apery sets are computed in a recursive way, and some tests to check whether given numerical semigroups are inductive or not are provided.

We characterize numerical semigroups of embedding dimension three having the same catenary and tame degrees., García Sánchez is supported by the projects MTM2010-15595, FQM-343, FQM-5849, and FEDER funds. The contents of this article are part of Viola’s master’s thesis. Part of this work was done while she visited the Univerisidad de Granada under the European Erasmus mobility program.

We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of computing the tame degree of an affine semigroup, and (iii) a dynamic algorithm to compute catenary degrees of affine semigroup elements. Our algorithms rely on theoretical results from combinatorial commutative algebra involving Gröbner bases, Hilbert bases, and other standard techniques. Implementation in the computer algebra system GAP is discussed.

La tragedie du Venezuela s’apparente a ce que Ricœur appelle le scandale du mal. Elle est marquee par la spoliation du domaine public et des violences multiples. Mais une transition est en marche.

Every almost symmetric numerical semigroup can be constructed by removing some minimal generators from an irreducible numerical semigroup with its same Frobenius number.

We give a positive answer to the Huneke–Wiegand Conjecture for monomial ideals over free numerical semigroup rings, and for two-generated monomial ideals over complete intersection numerical semigroup rings.

Let \({\mathbb K}\) be an algebraically closed field of characteristic zero and let \(f(x,y)=y^n+a_1(x)y^{n-1}+\dots +a_n(x)\) be a nonzero polynomial of \({\mathbb K}(\!(x)\!)[y]\) where \({\mathbb K}(\!(x)\!)\) denotes the field of meromorphic series in x.

Electronic version of an article published as Journal of Algebra and Its Applications, 15, 1, 2016, 1650007. DOI:10.1142/S0219498816500079 © World Scientific Publishing Company https://www.worldscientific.com/doi/abs/10.1142/S0219498816500079, In this paper, we find the ω-value of the generators of any numerical semigroup with embedding dimension three. This allows us to determine all possible orderings of the ω-values of the generators. In addition, we relate the ω-value of the numerical semigroup to its catenary degree., The first and third authors received National Science Foundation support under DMS-1262897. The second author is supported by the projects MTM2010-15595, FQM-343, FQM-5849, NSF-1061366 and FEDER funds.

Given a numerical semigroup $S$, we let $\mathrm P_S(x)=(1-x)\sum_{s\in S}x^s$ be its semigroup polynomial. We study cyclotomic numerical semigroups; these are numerical semigroups $S$ such that $\mathrm P_S(x)$ has all its roots in the unit disc. We conjecture that $S$ is a cyclotomic numerical semigroup if and only if $S$ is a complete intersection numerical semigroup and present some evidence for it. Aside from the notion of cyclotomic numerical semigroup we introduce the notion of cyclotomic exponents and polynomially related numerical semigroups. We derive some properties and give some applications of these new concepts., 17 pages, accepted for publication in SIAM J. Discrete Math

We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.

In this chapter we introduce the basic notions related to numerical semigroups. Numerical semigroups have not been always been referred to as such. In the past some authors called them semimodules, or demimodules and recently many authors (mainly those concerned with factorization properties) are starting to refer to them as numerical monoids.

The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers., 22 pages

We examine the Delta set of a cancellative and reduced atomic monoid S where every set of lengths of the factorizations of each element in S is bounded. In particular, we show the connection between the elements of �( S) and the Betti elements of S. We prove how the minimum and maximum element of �( S) can be determined using the Betti elements of S. This leads to a determination of when �( S) is a singleton. We then apply these results to the particular case where S is a numerical monoid that requires three generators. Conclusions are drawn in the cases where S has a unique minimal presentation, or has multiplicity three.

This paper presents a new methodology to compute the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius number) and multiplicity. First, we give theoretical results about the polynomial-time complexity of counting these semigroups. We also illustrate the methodology analyzing the cases of multiplicity 3 and 4 where some formulas for the number of numerical semigroups for any genus and Frobenius number are obtained.

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids., 22 pages