{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T11:18:06Z","timestamp":1772363886810,"version":"3.50.1"},"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 classify surjective lattice homomorphisms $W\\to W'$ between the weak orders on finite Coxeter groups. \u00a0Equivalently, we classify lattice congruences $\\Theta$ on $W$ such that the quotient $W\/\\Theta$ is isomorphic to $W'$. \u00a0Surprisingly, surjective homomorphisms exist quite generally: \u00a0They exist if and only if the diagram of $W'$ is obtained from the diagram of $W$ by deleting vertices, deleting edges, and\/or decreasing edge labels. \u00a0A surjective homomorphism $W\\to W'$ is determined by its restrictions to rank-two standard parabolic subgroups of $W$. \u00a0Despite seeming natural in the setting of Coxeter groups, this determination in rank two is nontrivial. \u00a0Indeed, from the combinatorial lattice theory point of view, all of these classification results should appear unlikely a priori. \u00a0As an application of the classification of surjective homomorphisms between weak orders, we also obtain a classification of surjective homomorphisms between Cambrian lattices and a general construction of refinement relations between Cambrian fans.<\/jats:p>","DOI":"10.37236\/7914","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T02:14:15Z","timestamp":1578622455000},"source":"Crossref","is-referenced-by-count":2,"title":["Lattice Homomorphisms Between Weak Orders"],"prefix":"10.37236","volume":"26","author":[{"given":"Nathan","family":"Reading","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,5,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p23\/7836","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p23\/7836","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:14:22Z","timestamp":1579216462000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7914","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,17]]},"article-number":"P2.23"}}