5 citations · 18 across the 12 of their papers we have counts for
19 papers
A new iterative algorithm for comprehensive Grobner systems
Anna Maria Bigatti, Elisa Palezzato, Michele Torielli
A Comprehensive Grobner system for a parametric ideal I in K(A)[X] represents the collection of all Grobner bases of the ideals I' in K[X] obtained as the values of the parameters…
Lefschetz properties and the Jacobian algebra of 3-dimensional hyperplane arrangements
Simone Marchesi, Elisa Palezzato, Michele Torielli
In this article, we study the weak and strong Lefschetz of higher dimensional quotients and dimension 1 almost complete intersections. We then apply the obtained results to the stu…
Total outer-connected domination number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato +1
In this paper, we study the total outer-connected domination number of the middle graph of a simple graph and we obtain tight bounds for this number in terms of the order of the mi…
Connected and outer-connected domination number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato +1
In this paper, we study the notions of connected domination number and of outer-connected domination number for middle graphs. Indeed, we obtain tight bounds for this number in ter…
Total domination number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato +1
A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number…
The Generalized Sylvester's And Orchard Problems Via Discriminantal arrangement
Pragnya Das, Elisa Palezzato, Simona Settepanella
In 1989 Manin and Schechtman defined the discriminantal arrangement associated to a generic arrangement of hyperplanes in a -di…
Total dominator coloring number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato +1
A total dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic n…
Domination number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato +1
In this paper, we study the domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph. We also compute the domination nu…
-Lefschetz properties, sectional matrices and hyperplane arrangements
Elisa Palezzato, Michele Torielli
In this article, we study the -Lefschetz properties for non-Artinian algebras, proving that several known results in the Artinian case can be generalized in this setting. Moreov…
Domination for latin square graphs
Behnaz Pahlavsay, Elisa Palezzato, Michele Torielli
In combinatorics, a latin square is a matrix filled with n different symbols, each occurring exactly once in each row and exactly once in each column. Associated to eac…
Lefschetz Properties and Hyperplane Arrangements
Elisa Palezzato, Michele Torielli
In this article, we study the weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, proving that several results known in t…
Localization of plus-one generated arrangements
Elisa Palezzato, Michele Torielli
We study the classes of free and plus-one generated hyperplane arrangements. Specifically, we describe how to compute the associated prime ideals of the Jacobian ideal of such an a…
Combinatorially equivalent hyperplane arrangements
Elisa Palezzato, Michele Torielli
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number ha…
-tuple total domination number of rook's graphs
Behnaz Pahlavsay, Elisa Palezzato, Michele Torielli
A -tuple total dominating set (TDS) of a graph is a set of vertices in which every vertex in is adjacent to at least vertices in . The minimum size of a $k…
Hyperplane arrangements in CoCoA
Elisa Palezzato, Michele Torielli
We introduce the package \textbf{arrangements} for the software CoCoA. This package provides a data structure and the necessary methods for working with hyperplane arrangements. In…
Free hyperplane arrangements over arbitrary fields
Elisa Palezzato, Michele Torielli
In this paper, we study the class of free hyperplane arrangements. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness ov…
New characterizations of freeness for hyperplane arrangements
Anna Maria Bigatti, Elisa Palezzato, Michele Torielli
In this article we describe two new characterizations of freeness for hyperplane arrangements via the study of the generic initial ideal and of the sectional matrix of the Jacobian…
Computing and Using Minimal Polynomials
John Abbott, Anna Maria Bigatti, Elisa Palezzato +1
Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I. Searching for a univariate polynomial in I is a particular ca…
Extremal behaviour in sectional matrices
Anna Maria Bigatti, Elisa Palezzato, Michele Torielli
In this paper we want to revive the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprov…