- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
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. © 2016 Elsevier Inc. All rights reserved.
4. The reverse lexicographic order
We have reg(I) = reg(gI) for any ideal I and a coordinate transformation g ∈ GLn because the Betti tables of I and gI coincide. However, taking the initial ideal does not commute with coordinate transformation because syzygy calculations are not preserved under coordinate transformations. Where reg(I) ≤ reg(inτ (I)) for any order τ , the following theorem of Bayer and Stillman shows that the graded reverse lexicographic order gives the lowest possible regularity for generic initial ideals.