Two remarks on monomial Gotzmann sets

A homogeneous set of monomials in a quotient of the polynomial ring S:=F[x1,…,xn] is called Gotzmann if the size of this set grows minimally when multiplied with the variables. We note that Gotzmann sets in the quotient arise from certain Gotzmann sets in S. Secondly, we prove a combinatorial result about the deletion of a variable in a Gotzmann set in S.