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Projective dimension and Castelnuovo-Mumford regularity of t-spread ideals

Autor: Amata, Luca, Crupi, Marilena, Ficarra, Antonino

We study some algebraic invariants of $t$-spread ideals, $t\ge 1$, such as the projective dimension and the Castelnuovo-Mumford regularity, by means of well-known graded resolutions. We state upper bounds for these invariants and, furthermore, we ide

Externí odkaz: http://arxiv.org/abs/2203.07084

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Cohen-Macaulay generalized binomial edge ideals

Autor: Amata, Luca, Crupi, Marilena, Rinaldo, Giancarlo

Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal associated to $G$ in the polynomial ring $K[x_{ij}, 1\le i \le m, 1\le j \le n]$. We classify the Cohen-Macaulay generalized binomial edge ideals. More

Externí odkaz: http://arxiv.org/abs/2112.15136

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Computational methods for t-spread monomial ideals

Autor: Amata, Luca

Let $K$ be a field and $S=K[x_1,\ldots,x_n]$ a standard polynomial ring over $K$. In this paper, some new optimized algorithms to compute the smallest $t$-spread lexicographic set and the smallest $t$-spread strongly stable set containing a given set

Externí odkaz: http://arxiv.org/abs/2110.11801

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A numerical characterization of the extremal Betti numbers of $t$-spread strongly stable Ideals

Autor: Amata, Luca, Ficarra, Antonino, Crupi, Marilena

Let $K$ be a field and let $S=K[x_1,\dots,x_n]$ be a standard polynomial ring over a field $K$. We characterize the extremal Betti numbers, values as well positions, of a $t$-spread strongly stable ideal of $S$. Our approach is constructive. Indeed,

Externí odkaz: http://arxiv.org/abs/2105.11944

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Upper bounds for Extremal Betti Numbers of $t$-Spread Strongly Stable Ideals

Autor: Amata, Luca, Ficarra, Antonino, Crupi, Marilena

We study the extremal Betti numbers of the class of $t$--spread strongly stable ideals. More precisely, we determine the maximal number of admissible extremal Betti numbers for such ideals, and thereby we generalize the known results for $t\in \{1,2\

Externí odkaz: http://arxiv.org/abs/2102.07462

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On the extremal Betti numbers of squarefree monomial ideals

Autor: Amata, Luca, Crupi, Marilena

Publikováno v: Int. Electron. J. Algebra 30 (2021), 168-202

Let $K$ be a field and $S = K[x_1,\dots,x_n]$ be a polynomial ring over $K$. We discuss the behaviour of the extremal Betti numbers of the class of squarefree strongly stable ideals. More precisely, we give a numerical characterization of the possibl

Externí odkaz: http://arxiv.org/abs/2102.06426

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Akademický článek

A generalization of Kruskal–Katona’s theorem

Autor: Amata Luca, Crupi Marilena

Publikováno v: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 28, Iss 2, Pp 35-51 (2020)

Let K be a field, E the exterior algebra of a finite dimensional K-vector space, and F a finitely generated graded free E-module with homogeneous basis g1, . . ., gr such that deg g1 ≤ deg g2 ≤ · · · ≤ deg gr. We characterize the Hilbert fun

Externí odkaz: https://doaj.org/article/d5c78efa3ef94ae1be2d5d54bf5e2341