{"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>Let $P\\left( m,n\\right) $ denote the maximum permanent of an $n$-by-$n$ lower Hessenberg $(0,1) $-matrix with $m$ entries equal to 1.  A \"staircased\" structure for some matrices achieving this maximum is obtained, and recursive formulas for computing $P\\left( m,n\\right) $ are given.  This structure and results about permanents are used to determine the exact values of $P\\left( m,n\\right) $ for $n \\leq m \\leq 8n\/3$ and for all $\\hbox{nnz}(H_n)-\\hbox{nnz}(H_{\\lfloor n\/2 \\rfloor}) \\leq m \\leq \\hbox{nnz}(H_n)$, where $\\hbox{nnz}(H_n)=(n^2+3n-2)\/2$ is the maximum number of ones in an $n$-by-$n$ Hessenberg $(0,1)$-matrix.<\/jats:p>","DOI":"10.37236\/1967","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:08:22Z","timestamp":1578701302000},"source":"Crossref","is-referenced-by-count":0,"title":["Permanents of Hessenberg (0,1)-matrices"],"prefix":"10.37236","volume":"12","author":[{"given":"D. D.","family":"Olesky","sequence":"first","affiliation":[]},{"given":"Bryan","family":"Shader","sequence":"additional","affiliation":[]},{"given":"P.","family":"Van den Driessche","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,12,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r70\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r70\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:39:26Z","timestamp":1579304366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1967","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,12,13]]},"article-number":"R70"}}