{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813680,"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>Given two positive integers $m\\le n$, we consider the set of partitions $\\lambda=(\\lambda_1,\\dots,\\lambda_\\ell,0,\\dots)$, $\\lambda_1\\ge\\lambda_2\\ge\\dots$, of $n$ such that the sum of its parts over a fixed increasing subsequence $(a_j)$ is $m$: $\\lambda_{a_1}+\\lambda_{a_2}+\\dots=m$.  We show that the number of such partitions does not depend on $n$ if $m$ is either constant and small relatively to $n$ or depend on $n$ but is close to its largest possible value: $n-ma_1=k$ for fixed $k$ (in the latter case some additional requirements on the sequence $(a_j)$ are needed).  This number is equal to the number of so-called colored partitions of $m$ (respectively $k$). It is proved by constructing bijections between these objects.<\/jats:p>","DOI":"10.37236\/1974","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:51Z","timestamp":1578719511000},"source":"Crossref","is-referenced-by-count":0,"title":["Integer Partitions with Fixed Subsums"],"prefix":"10.37236","volume":"12","author":[{"given":"Yu.","family":"Yakubovich","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,5,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:49:43Z","timestamp":1579322983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1n7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1974","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,5,16]]},"article-number":"N7"}}