{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:15:37Z","timestamp":1759335337230,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the generating function, an asymptotic formula for the enumeration function, and several combinatorial inequalities.<\/jats:p>","DOI":"10.37236\/4970","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:30:28Z","timestamp":1578699028000},"source":"Crossref","is-referenced-by-count":9,"title":["Distinct Parts Partitions without Sequences"],"prefix":"10.37236","volume":"22","author":[{"given":"Kathrin","family":"Bringmann","sequence":"first","affiliation":[]},{"given":"Karl","family":"Mahlburg","sequence":"additional","affiliation":[]},{"given":"Karthik","family":"Nataraj","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,7,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:14:20Z","timestamp":1579256060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/4970","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,7,1]]},"article-number":"P3.3"}}