Author
Monica La Barbiera
Bio: Monica La Barbiera is an academic researcher from University of Messina. The author has contributed to research in topics: Polynomial ring & Monomial. The author has an hindex of 4, co-authored 24 publications receiving 53 citations.
Papers
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TL;DR: In this article, the authors consider monomial ideals of mixed products in the polynomial ring in two sets of variables and investigate when they are generated by an s-sequence in order to compute invariants of their symmetric algebra.
Abstract: We consider monomial ideals of mixed products in the polynomial ring in two sets of variables and we investigate when they are generated by an s-sequence in order to compute invariants of their symmetric algebra.
11 citations
Journal Article•
TL;DR: In this article, the authors classify the unmixed ideals of Veronese bi-type and in some cases give a description of their associated prime ideals, and give a classification of the ideals of the bi-types.
Abstract: We classify the unmixed ideals of Veronese bi-type and in some cases we give a description of their associated prime ideals.
6 citations
Posted Content•
TL;DR: In this article, the notion of linear quotients is used to define classes of connected graphs whose monomial edge ideals, not necessarily square-free, have linear resolution, in order to compute standard algebraic invariants of the polynomial ring related to these graphs modulo such ideals.
Abstract: We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the polynomial ring related to these graphs modulo such ideals. Moreover we are able to determine the structure of the ideals of vertex covers for the edge ideals associated to the previous classes of graphs which can have loops on any vertex. Lastly, it is showed that these ideals are of linear type.
5 citations
Journal Article•
TL;DR: In this article, it was shown that if I is M -primary, then these polynomial functions have the same degree for all i. And if I am M-primary, the Betti numbers b_i(I^k ) of I^k are polynomials for k>>0.
Abstract: Let A=K[x1, ..... ,xn] be a standard graded polynomial ring over a field K , let M = (x_1, .... , x_n) be the graded maximal ideal and I a graded ideal of A . For each i the Betti numbers b_i(I^k ) of I^k are polynomial functions for k>>0 . We show that if I is M -primary, then these polynomial functions have the same degree for all i .
4 citations
TL;DR: In this paper, the authors investigated some classes of monomial ideals of S in order to classify ideals of the linear type and showed that these classes of ideals can be classified into linear and non-linear classes.
Abstract: Let S=K[x1,…,xn;y1,…,ym] be the polynomial ring in 2 sets of variables over a field K. We investigate some classes of monomial ideals of S in order to classify ideals of the linear type.
4 citations
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26 Mar 2015
TL;DR: In this paper, the authors show how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs, and directly link the algebraic properties of monomial algebraic structures to combinatorical structures (such as simplicial complexes, posets, digraphs, graphs, and clutters).
Abstract: Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It directly links the algebraic properties of monomial algebras to combinatorial structures (such as simplicial complexes, posets, digraphs, graphs, and clutters) and linear optimization problems.
60 citations
TL;DR: In this paper, the Kodiyalam polynomials were studied for a regular local ring and a graded ideal I in the polynomial ring, and it was shown that the limiting behavior depends only on the coefficients on the Kodyanomials in the highest possible degree.
14 citations
01 Jan 2010
TL;DR: In this article, the authors studied the symmetric algebra of these classes of monomial ideals and gave the conditions such that Iq,s is generated by an s-sequence.
Abstract: Let R = K[X1, . . . , Xn;Y1, . . . , Ym] be a polynomial ring in two sets of variables. Let r, k ≥ 1 be integers, then Ir,s is the Veronese-type ideal generated on degree r by the set {X1 1 . . . X ain n | ∑n j=1 aij = r, 0 ≤ aij ≤ s, s ∈ {1, . . . , r}} and Jk,s is the Veronese-type ideal generated on degree k by the set {Y bi1 1 . . . Y bim m | ∑m j=1 bij = k, 0 ≤ bij ≤ s, s ∈ {1, . . . , k}}. In [10] the author introduced the Veronese bi-type ideals Lq,s = ∑ r+k=q Ir,sJk,s generated in the same degree q. For s = 2 the Veronese bi-type ideals are the ideals of the walks of a bipartite graph with loops. In [9] the author studies the combinatorics of the integral closure and the normality of Lq,2. More in general, in [10] the same problem is studied for Lq,s for all s. In this paper we are interested to study the symmetric algebra of these classes of monomial ideals. In order to compute the standard invariants we investigate in which cases these monomial ideals are generated by s-sequences. In [6] the notion of s-sequences has been employed to compute the invariants of the symmetric algebra of finitely generated modules. The proposal is to compute standard invariants of the symmetric algebra in terms of the corresponding invariants of special quotients of the ring R. This computation can be obtained for finitely generated R-modules generated by an s-sequence. In Section 1 we consider the ideals of Veronese-type Iq,s. We give the conditions such that Iq,s is generated by an s-sequence. Then we compute standard algebraic invariants of the symmetric algebra of Iq,s.
11 citations
Journal Article•
TL;DR: In this paper, the notion of s-sequence is explored for edge ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding quotients of the polynomial ring related to the graphs.
Abstract: In this work we deal with the symmetric algebra of monomial ideals that arise from graphs, the edge ideals. The notion of s-sequence is explored for such ideals in order to compute standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of special quotients of the polynomial ring related to the graphs.
9 citations
TL;DR: In this paper, a numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely generated graded free S -module is given, where S is a polynomial ring in n variables over a field K of characteristic 0.
9 citations