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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 R:=F[x1,…,xn]/(x1a) 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.