Geodesic
A combinatorial approach to the Groebner bases for ideals generated by elementary symmetric functions
AJ Bu1
1Rutgers University
The electronic journal of combinatorics, Tome 29 (2022) no. 3

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl DOI arXiv
Previous work by Mora and Sala provides the reduced Groebner basis of the ideal formed by the elementary symmetric polynomials in $n$ variables of degrees $k=1,\dots,n$, $\langle e_{1,n}(x), \dots, e_{n,n}(x) \rangle$. Haglund, Rhoades, and Shimonozo expand upon this, finding the reduced Groebner basis of the ideal of elementary symmetric polynomials in $n$ variables of degree $d$ for $d=n-k+1,\dots,n$ for $k\leq n$. In this paper, we further generalize their findings by using symbolic computation and experimentation to conjecture the reduced Groebner basis for the ideal generated by the elementary symmetric polynomials in $n$ variables of arbitrary degrees and prove that it is a basis of the ideal.
DOI : 10.37236/10862
Classification : 05E05, 13P10
Mots-clés : homogeneous symmetric polynomial, Maple functions

AJ Bu  1

1 Rutgers University 
AJ Bu. A combinatorial approach to the Groebner bases for ideals generated by elementary symmetric functions. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10862
@article{10_37236_10862,
     author = {AJ Bu},
     title = {A combinatorial approach to the {Groebner} bases for ideals generated by elementary symmetric functions},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {3},
     doi = {10.37236/10862},
     zbl = {1492.05156},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10862/}
}
TY  - JOUR
AU  - AJ Bu
TI  - A combinatorial approach to the Groebner bases for ideals generated by elementary symmetric functions
JO  - The electronic journal of combinatorics
PY  - 2022
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/10862/
DO  - 10.37236/10862
ID  - 10_37236_10862
ER  - 
%0 Journal Article
%A AJ Bu
%T A combinatorial approach to the Groebner bases for ideals generated by elementary symmetric functions
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10862/
%R 10.37236/10862
%F 10_37236_10862

Cité par Sources :