{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:14Z","timestamp":1753893794253,"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>Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1\/N$. Let the $i$th cell contain $m_i$ particles on completion. Then associate with this cell the probability $a_i=m_i\/m$ and withdraw the particles.2. The other $n$ particles are then allocated polynomially, that is, the probability of a particle falling into the $i$th cell is $a_i$.Let $\\nu=\\nu(m,N)$ be the number of the first particle that falls into a non-empty cell during the second stage.  We give exact and asymptotic expressions for the expectation ${\\bf E}\\nu$.<\/jats:p>","DOI":"10.37236\/1714","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:29:07Z","timestamp":1578709747000},"source":"Crossref","is-referenced-by-count":2,"title":["Two-Stage Allocations and the Double $Q$-Function"],"prefix":"10.37236","volume":"10","author":[{"given":"Sergey","family":"Agievich","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,5,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:08:00Z","timestamp":1579324080000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1714","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,5,12]]},"article-number":"R21"}}