A combinatorial problem involving monomial ideals Original Research Article

In this paper, we consider monomial ideals in k[x1,x2,x3]. For each d ≥ 1, we compute the smallest number of monic monomials of degree d − 1 such that the ideal which they generate contains all monomials of degree d. This answers, for the case n = 3, a question posed by A.V. Geramita, D. Gregory, and L. Roberts.