In this paper, the authors present a completely explicit description of reduced Gröbner bases of the ideal of polynomials, which vanish on the set of characteristic vectors of the family of all d element subsets of the set 1, … , n.

An interesting feature of the result is that the bases are largely independent of the monomial order selected. The bases depend only on the ordering of the variables. As applications of this finding, the authors include some simple proofs of some known results on incidence matrices.