{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833644,"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>The labeled factorizations of a positive integer $n$ are obtained as a completion of the set of ordered factorizations of $n$. This follows a new technique for generating ordered factorizations found by extending a method for unordered factorizations that relies on partitioning the multiset of prime factors of $n$. Our results include explicit enumeration formulas and some combinatorial identities. It is proved that labeled factorizations of $n$ are equinumerous with the systems of complementing subsets of $\\{0,1,\\dots,n-1\\}$. We also give a new combinatorial interpretation of a class of generalized Stirling numbers.<\/jats:p>","DOI":"10.37236\/139","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:32:13Z","timestamp":1578717133000},"source":"Crossref","is-referenced-by-count":2,"title":["Labeled Factorization of Integers"],"prefix":"10.37236","volume":"16","author":[{"given":"Augustine O.","family":"Munagi","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,4,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:56:06Z","timestamp":1579316166000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/139","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,4,22]]},"article-number":"R50"}}