Published: July 1, 2022 in Volume 29 (2022), Issue 3 of The Electronic Journal of Combinatorics
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,...,n. 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,...,n for k=n. In this paper, we further generalize their findings by using symbolic computation and experimentation to construct the reduced Groebner basis for the ideal generated by the elementary symmetric polynomials in n variables of arbitrary degrees.