{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:04Z","timestamp":1753893784357,"version":"3.41.2"},"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>Let $Y=(X, \\{ R_i \\}_{1\\le i\\le D})$ denote a symmetric association scheme, and assume that $Y$ is $Q$-polynomial with respect to an ordering $E_0,...,E_D$ of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities $m_i$ $(0 \\leq i \\leq D)$ of $Y$ is unimodal. Talking to Terwilliger, Stanton made the related conjecture that $m_i \\leq m_{i+1}$ and $m_i \\leq m_{D-i}$ for $i  &lt;  D\/2$. We prove that if $Y$ is dual-thin in the sense of Terwilliger, then the Stanton conjecture is true.<\/jats:p>","DOI":"10.37236\/1589","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:16Z","timestamp":1578708556000},"source":"Crossref","is-referenced-by-count":2,"title":["The Multiplicities of a Dual-thin $Q$-polynomial Association Scheme"],"prefix":"10.37236","volume":"8","author":[{"given":"Bruce E.","family":"Sagan","sequence":"first","affiliation":[]},{"given":"John S.","family":"Caughman, IV","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,1,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1n4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1n4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:17Z","timestamp":1579324817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1n4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1589","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,1,28]]},"article-number":"N4"}}