{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T12:18:44Z","timestamp":1773922724159,"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>The Jacobi-Stirling numbers of the first and second kinds were introduced in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers.  Andrews and Littlejohn have recently given a combinatorial interpretation for the second kind of the latter numbers.  Noticing that these numbers are very similar to the classical central factorial numbers, we give combinatorial interpretations for the Jacobi-Stirling numbers of both kinds, which provide a unified treatment of the combinatorial theories for the two previous sequences and also for the Stirling numbers of both kinds.<\/jats:p>","DOI":"10.37236\/342","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:13:31Z","timestamp":1578716011000},"source":"Crossref","is-referenced-by-count":29,"title":["Combinatorial Interpretations of the Jacobi-Stirling Numbers"],"prefix":"10.37236","volume":"17","author":[{"given":"Yoann","family":"Gelineau","sequence":"first","affiliation":[]},{"given":"Jiang","family":"Zeng","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,5,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r70\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r70\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:53:42Z","timestamp":1579305222000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/342","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,5,14]]},"article-number":"R70"}}