{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:31Z","timestamp":1753893811879,"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>A Costas array of order $n$ is an $n\\times n$ permutation matrix such that all vectors between pairs of ones are distinct. Thus, a permutation matrix fails to be a Costas array if and only if it contains ones that form a (possibly degenerate) parallelogram. In this paper, we enumerate parallelograms in an $n\\times n$ permutation matrix. We use our new formulas to improve Davies's $O(n^{-1})$ result for the density of Costas arrays.<\/jats:p>","DOI":"10.37236\/5610","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T16:42:51Z","timestamp":1578674571000},"source":"Crossref","is-referenced-by-count":6,"title":["Enumeration of Parallelograms in Permutation Matrices for Improved Bounds on the Density of Costas Arrays"],"prefix":"10.37236","volume":"23","author":[{"given":"Christopher N.","family":"Swanson","sequence":"first","affiliation":[]},{"given":"Bill","family":"Correll, Jr.","sequence":"additional","affiliation":[]},{"given":"Randy W.","family":"Ho","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,3,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:31:27Z","timestamp":1579221087000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,4]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5610","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,3,4]]},"article-number":"P1.44"}}