Constructing a Gr\"obner basis of Griffin's ideal
Combinatorics
2023-08-01 v1
Abstract
In his Ph.D. thesis, Sean Griffin introduced a family of ideals and found monomial bases for their quotient rings. These rings simultaneously generalize the Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono and the cohomology rings of Springer fibers studied by Tanisaki and Garsia-Procesi. We recursively construct a Gr\"{o}bner basis of Griffin's ideals with respect to the graded reverse lexicographical order. Consequently, Griffin's monomial basis is the standard monomial basis. Coefficients of polynomials in our Gr\"{o}bner basis are integers and leading coefficients are one.
Keywords
Cite
@article{arxiv.2307.16046,
title = {Constructing a Gr\"obner basis of Griffin's ideal},
author = {Tianyi Yu},
journal= {arXiv preprint arXiv:2307.16046},
year = {2023}
}