Monica La Barbiera

Mixed Product Ideals Generated by s-Sequences

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.

Monomial Ideals of Graphs with Loops

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 shown that these ideals are of linear type.

Algebraic Properties of Universal Squarefree Lexsegment Ideals

Let K be a field and let A=K[X1,…,Xn] be the polynomial ring in X1,…,Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics computing some invariants. Moreover, we study the link between such a special class of squarefree lexsegment ideals and the so-called s-sequences.

On Standard Invariants of Bi-polymatroidal Ideals

The standard invariants of the bi-polymatroidal ideals of Veronese type are computed. 2010 Mathematics Subject Classification: 05B35, 13C15

Edge ideals and connection problems

Ideals arising from graphs are investigated via Grobner bases theory in order to introduce algebraic objects useful for applications related to the field of security. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of any graph G is considered, so that a description of the Grobner basis for the relation ideal J of the symmetric algebra of I(G) can be obtained. Based on this approach, the initial ideal of J with respect to a monomial order is well-determined and defines the edge ideal of a supporting graph F, essential in transmitting.

On the graphic realization of certain monomial sequences

d-sequences and s-sequences are important monomial sequences. In this paper, graphs that have edge ideals with generators forming d-sequences or s-sequences are examined. Two equivalent conditions are given.

On the symmetric algebras associated to graphs with loops

We study the symmetric algebra of monomial ideals that arise from graphs with loops. The notion of s-sequence is investigated 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.

On A Class of Vertex Cover Ideals

We investigate vertex cover ideals associated to a significative class of connected graphs. These ideals are stated to be Cohen-Macaulay and, using the notion of linear quotients, standard algebraic invariants for them are computed. Mathematics Subject Classification 2010: 05C25, 05E40, 13C14, 90B10.