Details:
Title  Hilbert ideals of vector invariants of $S_2$ and $S_3$.  Author(s)  "Ozgün "Unlü, Müfit Sezer  Type  Article in Journal  Abstract  The Hilbert ideal is the ideal generated by positive degree invariants of a finite group. We consider the vector invariants of the natural action of Sn. For S2 we compute the reduced and universal Gröbner bases for the Hilbert ideal. As well, we identify all initial form ideals of the Hilbert ideal and describe its Gröbner fan. In modular characteristics, we show that the Hilbert ideal for S3 can be generated by polynomials of degree at most three and the reduced Gröbner basis contains no polynomials that involve variables from four or more copies. Our results give support for conjectures for improved degree bounds and regularity conditions on the Gröbner bases for the Hilbert ideal of vector invariants of Sn.  Keywords  Hilbert ideals, vector invariants, symmetric groups.  ISSN  09495932 
URL 
http://www.heldermann.de/JLT/JLT22/JLT224/jlt22054.htm 
Language  English  Journal  J. Lie Theory  Volume  22  Number  4  Pages  11811196  Publisher  Heldermann, Lemgo  Year  2012  Edition  0  Translation 
No  Refereed 
No 
