{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:25Z","timestamp":1753893805563,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants.  We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants<\/jats:p>","DOI":"10.37236\/1877","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:17:46Z","timestamp":1578719866000},"source":"Crossref","is-referenced-by-count":0,"title":["Some New Methods in the Theory of $m$-Quasi-Invariants"],"prefix":"10.37236","volume":"11","author":[{"given":"J.","family":"Bell","sequence":"first","affiliation":[]},{"given":"A. M.","family":"Garsia","sequence":"additional","affiliation":[]},{"given":"N.","family":"Wallach","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:47:48Z","timestamp":1579322868000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2r20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,30]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1877","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,8,30]]},"article-number":"R20"}}