A combinatorial approach to the Groebner bases for ideals generated by elementary symmetric functions
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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
Mots-clés : homogeneous symmetric polynomial, Maple functions
Affiliations des auteurs :
AJ Bu 1
@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/}
}
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
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