{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:24Z","timestamp":1753893864964,"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>We associate to any given circulant complex matrix $C$ another one $E(C)$ such that\u00a0$E(E(C)) = C^{*}$ the transpose conjugate of $C.$ All circulant Hadamard matrices of order $4$\u00a0satisfy a condition $C_4$ on their eigenvalues, namely, the absolute value of the sum of all eigenvalues\u00a0is bounded above by $2.$ We prove by a \"descent\" that uses our operator $E$ that\u00a0the only circulant Hadamard matrices of order $n \\geq 4$, that satisfy a condition $C_n$ that generalizes the condition $C_4$ and that consist of a list of $n\/4$ inequalities for the absolute value of some sums of eigenvalues of $H$ are the known ones.<\/jats:p>","DOI":"10.37236\/5237","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T16:34:59Z","timestamp":1578674099000},"source":"Crossref","is-referenced-by-count":1,"title":["New Duality Operator for Complex Circulant Matrices and a Conjecture of Ryser"],"prefix":"10.37236","volume":"23","author":[{"given":"Luis H.","family":"Gallardo","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,3,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:30:55Z","timestamp":1579221055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5237","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,3,18]]},"article-number":"P1.59"}}