Turkish Journal of Mathematics
Abstract
The definition of a generic initial ideal includes the assumption $x_1>x_2> \cdots >x_n$. A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a permutation of the variables.
DOI
10.3906/mat-2008-106
Keywords
Generic initial ideals, Zariski open sets, permutation of variables
First Page
1444
Last Page
1448
Recommended Citation
DANIŞ, B (2021). A short note on generic initial ideals. Turkish Journal of Mathematics 45 (3): 1444-1448. https://doi.org/10.3906/mat-2008-106
