{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T10:30:15Z","timestamp":1780482615311,"version":"3.54.1"},"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>There are several classes of ranked posets related to reflection groups which are known to have the Sperner property, including the Bruhat orders and the generalized noncrossing partition lattices (i.e., the maximal intervals in absolute orders).\u00a0 In 2019, Harper\u2013Kim proved that the absolute orders on the symmetric groups are (strongly) Sperner.\u00a0 In this paper, we give an alternate proof that extends to the signed symmetric groups and the dihedral groups.\u00a0 Our simple proof uses techniques inspired by Ford\u2013Fulkerson's theory of networks and flows, and a product theorem.<\/jats:p>","DOI":"10.37236\/8874","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T12:55:38Z","timestamp":1595940938000},"source":"Crossref","is-referenced-by-count":1,"title":["The Absolute Orders on the Coxeter Groups $A_n$ and $B_n$ are Sperner"],"prefix":"10.37236","volume":"27","author":[{"given":"Lawrence H.","family":"Harper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gene B.","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Neal","family":"Livesay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2020,7,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p14\/8131","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p14\/8131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T12:55:54Z","timestamp":1595940954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,24]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8874","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,24]]},"article-number":"P3.14"}}