Turkish Journal of Mathematics
DOI
10.3906/mat-2008-106
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.
Keywords
Generic initial ideals, Zariski open sets, permutation of variables
First Page
1444
Last Page
1448
Recommended Citation
DANIŞ, BEKİR
(2021)
"A short note on generic initial ideals,"
Turkish Journal of Mathematics: Vol. 45:
No.
3, Article 22.
https://doi.org/10.3906/mat-2008-106
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss3/22
