{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:08Z","timestamp":1753893788104,"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>For $n$ a positive integer, we show that the number of of $2n$-tuples of integers that are the row and column sums of some $n\\times n$ matrix with entries in $\\{0,1\\}$ is evenly divisible by $n+1$. This confirms a conjecture of Benton, Snow, and Wallach. We also consider a $q$-analogue for $m\\times n$ matrices. We give an efficient recursion formula for this analogue. We prove a divisibility result in this context that implies the $n+1$ divisibility result.<\/jats:p>","DOI":"10.37236\/1146","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:02:30Z","timestamp":1578718950000},"source":"Crossref","is-referenced-by-count":3,"title":["On the Number of Possible Row and Column Sums of 0,1-Matrices"],"prefix":"10.37236","volume":"13","author":[{"given":"Daniel","family":"Goldstein","sequence":"first","affiliation":[]},{"given":"Richard","family":"Stong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,4,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:11:32Z","timestamp":1579320692000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1n8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1146","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,4,18]]},"article-number":"N8"}}