We deal with monomial ideals of mixed products to which it is possible associate a graph, the so-called generalized graph ideals; their generators are square-free monomials of fixed degree depending only on the graph. The problem is that to determine, in low degree q , the paths of length q-1 of any simple connected graph G and the generators of the corresponding generalized graph ideal I_q(G), through combinatorial calculations made only on the incidence matrix of G. Such a problem is fully solved for generalized graph ideals in degree less than 5; in these cases the number and the structure of the generators of that ideals are computed.
q-PATHS OF A GRAPH AND INCIDENCE MATRIX
IMBESI, Maurizio
2006-01-01
Abstract
We deal with monomial ideals of mixed products to which it is possible associate a graph, the so-called generalized graph ideals; their generators are square-free monomials of fixed degree depending only on the graph. The problem is that to determine, in low degree q , the paths of length q-1 of any simple connected graph G and the generators of the corresponding generalized graph ideal I_q(G), through combinatorial calculations made only on the incidence matrix of G. Such a problem is fully solved for generalized graph ideals in degree less than 5; in these cases the number and the structure of the generators of that ideals are computed.Pubblicazioni consigliate
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