{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848573,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $k \\leq n$ be nonnegative integers and let $\\lambda$ be a partition of $k$. S. Griffin recently introduced a quotient $R_{n,\\lambda}$ of the polynomial ring\u00a0 $\\mathbb{Q}[x_1, \\dots, x_n]$ in $n$ variables which simultaneously generalizes the\u00a0 Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono\u00a0and the cohomology rings of Springer fibers studied by Tanisaki and Garsia-Procesi. We describe the space $V_{n,\\lambda}$ of harmonics attached to $R_{n,\\lambda}$\u00a0 and produce a harmonic basis of $R_{n,\\lambda}$ indexed by certain ordered set partitions $\\mathcal{OP}_{n,\\lambda}$. The combinatorics of this basis is governed by a new extension of\u00a0 the Lehmer code\u00a0of a permutation to $\\mathcal{OP}_{n, \\lambda}$.<\/jats:p>","DOI":"10.37236\/9610","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T08:55:20Z","timestamp":1604048120000},"source":"Crossref","is-referenced-by-count":1,"title":["Harmonic Bases for Generalized Coinvariant Algebras"],"prefix":"10.37236","volume":"27","author":[{"given":"Brendon","family":"Rhoades","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianyi","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zehong","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,10,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p16\/8197","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p16\/8197","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T08:55:20Z","timestamp":1604048120000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9610","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,10,30]]},"article-number":"P4.16"}}