{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:28Z","timestamp":1753893868334,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Legendre-Stirling numbers of the second kind were introduced by Everitt et al. in the spectral theory of powers of the Legendre differential expressions. As a continuation of the work of Andrews and Littlejohn (Proc. Amer. Math. Soc., 137 (2009), 2581-2590), we provide a combinatorial code for Legendre-Stirling set partitions. As an application, we obtain expansions of the Legendre-Stirling numbers of both kinds in terms of binomial coefficients.<\/jats:p>","DOI":"10.37236\/8060","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:43:09Z","timestamp":1578667389000},"source":"Crossref","is-referenced-by-count":1,"title":["On Certain Combinatorial Expansions of the Legendre-Stirling Numbers"],"prefix":"10.37236","volume":"25","author":[{"given":"Shi-Mei","family":"Ma","sequence":"first","affiliation":[]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Yeong-Nan","family":"Yeh","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,12,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p57\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p57\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:19:14Z","timestamp":1579234754000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,21]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/8060","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,12,21]]},"article-number":"P4.57"}}