PARTIAL EQUATION SYSTEMS ASSOCIATED TO DIRECTED GRAPHS

Let G be a directed graph with m vertices and n edges, I(B) the binomial ideal associated to the incidence matrix B of the graph G, and I L the lattice ideal associated to the columns of the matrix B. Also let B i be a submatrix of B after removing the ith column. We study the rank of the space of solutions of binomial D- module associated to I(B i ) as A-graded ideal, where A is a matrix that, AB i = 0.