15 citations · 34 across the 16 of their papers we have counts for
22 papers
The structure of almost symmetric almost complete intersection numerical semigroups
Kazufumi Eto, Naoyuki Matsuoka, Alessio Moscariello +3
We prove a structure theorem for numerical semigroups H that are almost symmetric and almost complete intersections. We show that a row-factorization (RF) matrix of H must possess…
There is no polynomial formula for the catenary and the tame degree of finitely generated monoids
Alfred Geroldinger, Alessio Moscariello
In the last two decades there has been a wealth of results determining the precise value of the catenary degree and the tame degree. Mostly, however, only for very special classes…
An upper bound for the multiplicity and Wilf's conjecture for one-dimensional Cohen-Macaulay rings
Marco D'Anna, Alessio Moscariello
In this work we provide an upper bound for the multiplicity of a one-dimensional Cohen-Macaulay ring (under certain conditions), describe the rings attaining the equality for this…
Nearly Gorenstein numerical semigroups with five generators have bounded type
Alessio Moscariello, Francesco Strazzanti
We prove that the type of nearly Gorenstein numerical semigroups minimally generated by integers is bounded. In particular, if such a semigroup is not almost symmetric, then it…
Open problems on relations of numerical semigroups
Alessio Moscariello, Alessio Sammartano
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and assoc…
On minimal presentations of numerical monoids
Alessio Moscariello, Alessio Sammartano
We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. V…
F-threshold of determinantal rings
Barbara Betti, Alessio Moscariello, Francesco Romeo +1
In this paper, by using a combinatorial approach, we establish a new upper bound for the F-threshold $c^\mm(\mm)$ of determinantal rings generated by maximal minors. We prove that…
Bounds for syzygies of monomial curves
Giulio Caviglia, Alessio Moscariello, Alessio Sammartano
Let G be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the differenc…
On the boundedness of the type of an almost Gorenstein monomial curve in
Alessio Moscariello
We prove that the Cohen-Macaulay type of an almost Gorenstein monomial curve is bounded.
Bounds for invariants of numerical semigroups and Wilf's Conjecture
Marco D'Anna, Alessio Moscariello
Given coprime positive integers , the Frobenius number is the largest integer not representable as a linear combination of $g_1,\ldots,g_e…
Lacunary Polynomial Compositions
Alessio Moscariello
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and…
On sparse perfect powers
Alessio Moscariello
This work is devoted to proving that, given an integer , there are infinitely many perfect powers, coprime with , having exactly non-zero digits in their base…
Nearly Gorenstein vs almost Gorenstein affine monomial curves
Alessio Moscariello, Francesco Strazzanti
We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen-Macaulay type of a nearly Gorenstein monomi…
Delta sets for symmetric numerical semigroups with embedding dimension three
P. A. García-Sánchez, D. Llena, A. Moscariello
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…
Minimal relations and the Diophantine Frobenius Problem in embedding dimension three
Alessio Moscariello
This paper provides a formula for the minimal relations and the Frobenius number of a numerical semigroup minimally generated by three pairwise coprime positive integers.
On the type of an almost Gorenstein monomial curve
Alessio Moscariello
We prove that the Cohen-Macaulay type of an almost Gorenstein monomial curve is at most , and make some considerations on the general case.
Delta sets for numerical semigroups with embedding dimension three
Pedro A. García-Sánchez, David Llena, Alessio Moscariello
We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.
On a conjecture of Wilf about the Frobenius number
Alessio Moscariello, Alessio Sammartano
Given coprime positive integers , the Frobenius number is the largest integer which is not representable as a non-negative integer combination of the . Let…
On integers which are representable as sums of large squares
Alessio Moscariello
We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set is asymptotic…
Generators of a fraction of a numerical semigroup
Alessio Moscariello
Given a numerical semigroup and a positive integer , the fraction is again a numerical semigroup. In this paper we determi…
The first elements of the quotient of a numerical semigroup by a positive integer
Alessio Moscariello
Given three pairwise coprime positive integers we show the existence of a relation between the sets of the first elements of the three quotients $\fr…
On the least positive solution to a proportionally modular Diophantine inequality
Alessio Moscariello
Given three positive integers , a proportionally modular Diophantine inequality is an expression of the form . Our aim is to give a recursive formula for…