{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:23Z","timestamp":1753893863247,"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>We generalize the Tamari lattice by extending the notions of $231$-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients of the symmetric group $\\mathfrak{S}_{n}$.\u00a0 We show bijectively that these three objects are equinumerous.\u00a0 We show how to extend these constructions to parabolic quotients of any finite Coxeter group.\u00a0 The main ingredient is a certain aligned condition of inversion sets; a concept which can in fact be generalized to any reduced expression of any element in any (not necessarily finite) Coxeter group.<\/jats:p>","DOI":"10.37236\/7844","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:02:02Z","timestamp":1578636122000},"source":"Crossref","is-referenced-by-count":1,"title":["Tamari Lattices for Parabolic Quotients of the Symmetric Group"],"prefix":"10.37236","volume":"26","author":[{"given":"Henri","family":"M\u00fchle","sequence":"first","affiliation":[]},{"given":"Nathan","family":"Williams","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p34\/7959","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p34\/7959","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:01:22Z","timestamp":1579233682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,22]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7844","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,11,22]]},"article-number":"P4.34"}}