Antonino Ficarra

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20212026

most citedUpper bounds for Extremal Betti Numbers of

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-Spread Strongly Stable Ideals

4 citations · 17 across the 50 of their papers we have counts for

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14 papers · 1 filter

math.AC2023★ 1 cited

Ideals and their Fitting ideals

David Eisenbud, Antonino Ficarra, Jürgen Herzog +1

For an ideal $I$ in a Noetherian ring $R$ , the Fitting ideals $Fitt_{j} (I)$ are studied. We discuss the question of when $Fitt_{j} (I) = I$ or $\sqrt{\textrm{Fitt}_j(I)}…

math.AC2023★ 1 cited

Shellability of Componentwise Discrete Polymatroids

Antonino Ficarra

In the present paper, motivated by a conjecture of Jahan and Zheng, we prove that componentwise polymatroidal ideals have linear quotients. This solves positively a conjecture of B…

math.AC2023

Matching Powers: Macaulay2 Package

Antonino Ficarra

We introduce the Macaulay2 package MatchingPowers. It allows to compute and manipulate the matching powers of a monomial ideal. The basic theory of matching powers is explained and…

math.AC2023

Homological Shift Ideals: Macaulay2 Package

Antonino Ficarra

We introduce the Macaulay2 package HomologicalShiftIdeals. It allows to compute the homological shift ideals of a monomial ideal, and to check the homological shift properties, inc…

math.AC2023

The eventual shape of the Betti table of $m^{k} M$

Antonino Ficarra, Jürgen Herzog, Somayeh Moradi

Let $S$ be the polynomial ring over a field $K$ in a finite set of variables, and let $m$ be the graded maximal ideal of $S$ . It is known that for a finitely generated…

math.AC2023

Matching powers of monomial ideals and edge ideals of weighted oriented graphs

Nursel Erey, Antonino Ficarra

We introduce the concept of matching powers of monomial ideals. Let $I$ be a monomial ideal of $S = K [x_{1}, \dots, x_{n}]$ , with $K$ a field. The $k$ th matching power of $I$ is the monomi…

math.AC2023

Very well-covered graphs via the Rees algebra

Marilena Crupi, Antonino Ficarra

A very well-covered graph is a well-covered graph without isolated vertices such that the size of its minimal vertex covers is half of the number of vertices. If $G$ is a Cohen-Mac…

math.AC2023

The toric ring of one dimensional simplicial complexes

Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate

Let $Δ$ be a 1-dimensional simplicial complex. Then $Δ$ may be identified with a finite simple graph $G$ . In this article, we investigate the toric ring $R_{G}$ of $G$ . All graphs $G…

math.AC2023

Asymptotic behaviour of the $v$ -number of homogeneous ideals

Antonino Ficarra, Emanuele Sgroi

Let $I$ be a graded ideal of a standard graded polynomial ring $S$ with coefficients in a field $K$ . The asymptotic behaviour of the $v$ -number of the powers of $I$ is inves…

math.AC2023★ 2 cited

Matchings, Squarefree Powers and Betti Splittings

Marilena Crupi, Antonino Ficarra, Ernesto Lax

Let $G$ be a finite simple graph and let $I (G)$ be its edge ideal. In this article, we deeply investigate the squarefree powers of $I (G)$ by means of Betti splittings. When $G$ is…

math.AC2023

Very well-covered graphs by Betti splittings

Marilena Crupi, Antonino Ficarra

A very well-covered graph is an unmixed graph without isolated vertices such that the height of its edge ideal is half of the number of vertices. We study these graphs by means of…

math.AC2023★ 1 cited

Mapping cones of monomial ideals over exterior algebras

Marilena Crupi, Antonino Ficarra, Ernesto Lax

Let $K$ be a field, $V$ a finite dimensional $K$ -vector space and $E$ the exterior algebra of $V$ . We analyze iterated mapping cone over $E$ . If $I$ is a monomial ideal of $E$ with…

math.AC2023

Macaulay's theorem for vector-spread algebras

Marilena Crupi, Antonino Ficarra, Ernesto Lax

Let $S = K [x_{1}, \dots, x_{n}]$ be the standard graded polynomial ring, with $K$ a field, and let $t = (t_{1}, \dots, t_{d - 1}) \in Z_{\geq 0}^{d - 1}$ , $d \geq 2$ , be a $(d - 1)$ -tuple…

math.AC2023

The size of the Betti table of Binomial Edge Ideals

Antonino Ficarra, Emanuele Sgroi

Let $G$ be a finite simple graph on $n$ non-isolated vertices, and let $J_{G}$ be its binomial edge ideal. We determine almost all pairs $(projdim (J_{G}), reg (J_{G}))$ , wher…

Ideals and their Fitting ideals

Shellability of Componentwise Discrete Polymatroids

Matching Powers: Macaulay2 Package

Homological Shift Ideals: Macaulay2 Package

The eventual shape of the Betti table of mkM

Matching powers of monomial ideals and edge ideals of weighted oriented graphs

Very well-covered graphs via the Rees algebra

The toric ring of one dimensional simplicial complexes

Asymptotic behaviour of the v-number of homogeneous ideals

Matchings, Squarefree Powers and Betti Splittings

Very well-covered graphs by Betti splittings

Mapping cones of monomial ideals over exterior algebras

Macaulay's theorem for vector-spread algebras

The size of the Betti table of Binomial Edge Ideals

The eventual shape of the Betti table of $m^{k} M$

Asymptotic behaviour of the $v$ -number of homogeneous ideals