{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:29Z","timestamp":1753893869870,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $r$ and $n$ be positive integers, let $G_n$ be the complex reflection group of $n \\times n$ monomial matrices whose entries are $r^{\\textrm{th}}$ roots of unity and let $0 \\leq k \\leq n$ be an integer. Recently, Haglund, Rhoades and Shimozono ($r=1$) and Chan and Rhoades ($r&gt;1$) introduced quotients $R_{n,k}$ (for $r&gt;1$) and $S_{n,k}$ (for $r \\geq 1$) of the polynomial ring $\\mathbb{C}[x_1,\\ldots,x_n]$ in $n$ variables, which for $k=n$ reduce to the classical coinvariant algebra attached to $G_n$. When $n=k$ and $r=1$, Garsia and Stanton exhibited a quotient of $\\mathbb{C}[\\mathbf{y}_S]$ isomorphic to the coinvariant algebra, where $\\mathbb{C}[\\mathbf{y}_S]$ is the polynomial ring in $2^n-1$ variables whose variables are indexed by nonempty subsets $S \\subseteq [n]$. In this paper, we will define analogous quotients that are isomorphic to $R_{n,k}$ and $S_{n,k}$.<\/jats:p>","DOI":"10.37236\/8109","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:06:16Z","timestamp":1578639976000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized Coinvariant Algebras for $G(r,1,n)$ in the Stanley-Reisner setting"],"prefix":"10.37236","volume":"26","author":[{"given":"Dani\u00ebl","family":"Kroes","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,7,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p11\/7871","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p11\/7871","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:11:49Z","timestamp":1579234309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,5]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/8109","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,7,5]]},"article-number":"P3.11"}}