Abstract
Bayer–Stillman showed that reg(I)=reg(ginτ(I)) when τ is the graded reverse lexicographic order. We show that the reverse lexicographic order is the unique monomial order τ satisfying reg(I)=reg(ginτ(I)) for all ideals I. We also show that if ginτ1(I)=ginτ2(I) for all I, then τ1=τ2.
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