{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:54:46Z","timestamp":1772517286265,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>It is shown that the numbers $c_i$ of chains of length $i$ in the proper part $L\\setminus\\{0,1\\}$ of a distributive  lattice $L$ of length $\\ell +2$ satisfy the inequalities $$c_0 &lt; \\ldots &lt; c_{\\lfloor{\\ell \/2}\\rfloor} \\quad\\hbox{ and }\\quad c_{\\lfloor{3 \\ell \/4}\\rfloor}&gt;\\ldots&gt;c_{\\ell}.$$ This proves 75% of the inequalities implied by the  Neggers unimodality conjecture.<\/jats:p>","DOI":"10.37236\/1971","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:18:25Z","timestamp":1578719905000},"source":"Crossref","is-referenced-by-count":3,"title":["Chain Polynomials of Distributive Lattices are 75% Unimodal"],"prefix":"10.37236","volume":"12","author":[{"given":"Anders","family":"Bj\u00f6rner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan David","family":"Farley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,3,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:50:48Z","timestamp":1579323048000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1n4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1971","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3,14]]},"article-number":"N4"}}