Generating monomials in dimensions three and four Original Research Article

We introduce a technique to determine a lower bound on the number of monomials of degree d − 1 in n variables needed to generate all monomials of degree d. For n = 3, this gives a new proof of a result by Curtis and for n = 4, it improves the lower bound of Geramita et al. (1986). We also give a cover for the dimension four case that improves the upper bound given in the paper by Geramita and others.