{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835635,"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 rational matrix is totally dyadic if all of its nonzero subdeterminants are in $\\{\\pm 2^k\\ :\\ k \\in {\\bf Z}\\}$. An oriented matriod is dyadic if it has a totally dyadic representation $A$. A dyadic oriented matriod is dyadic of order $k$ if it has a totally dyadic representation $A$ with full row rank and with the property that for each pair of adjacent bases $A_1$ and $A_2$ $$2^{-k} \\le \\left| { {\\det(A_1)} \\over {\\det(A_2)}}\\right|\\le 2^k.$$ In this note we present a counterexample to a conjecture on the relationship between the order of a dyadic oriented matroid and the ratio of agreement to disagreement in sign of its signed circuits and cocircuits (Conjecture 5.2, Lee (1990)).<\/jats:p>","DOI":"10.37236\/1455","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:00:47Z","timestamp":1578708047000},"source":"Crossref","is-referenced-by-count":0,"title":["On a Conjecture Concerning Dyadic Oriented Matroids"],"prefix":"10.37236","volume":"6","author":[{"given":"Matt","family":"Scobee","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,3,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:33:14Z","timestamp":1579325594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,3,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1455","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,3,30]]},"article-number":"R23"}}