{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:42Z","timestamp":1759335942362,"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>We present a natural extension of Andrews' multiple sums counting partitions of the form $(\\lambda_1,\\cdots,\\lambda_m)$ with $\\lambda_i\\geq \\lambda_{i+k-1}+2$. The multiple sum that we construct is the generating function for the so-called $K$-restricted jagged partitions.  A jagged partition is a sequence of non-negative integers $(n_1,n_2,\\cdots , n_m)$ with $n_m\\geq 1$ subject to the weakly decreasing conditions $n_i\\geq n_{i+1}-1$ and $n_i\\geq n_{i+2}$. The $K$-restriction refers to the following additional conditions: $n_i \\geq n_{i+K-1} +1$ or  $n_i = n_{i+1}-1 = n_{i+K-2}+1= n_{i+K-1}$. The corresponding generalization of the Rogers-Ramunjan identities is displayed, together with a novel combinatorial interpretation.<\/jats:p>","DOI":"10.37236\/1909","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:19:07Z","timestamp":1578719947000},"source":"Crossref","is-referenced-by-count":10,"title":["Generating Function for $K$-Restricted Jagged Partitions"],"prefix":"10.37236","volume":"12","author":[{"given":"J.-F.","family":"Fortin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Jacob","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Mathieu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,2,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:51:00Z","timestamp":1579323060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,2,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1909","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,2,21]]},"article-number":"R12"}}