{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:57Z","timestamp":1753893777100,"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 consider the problem of determining when two delta-matroids on the same ground-set have a common base. Our approach is to adapt the theory of matchings in 2-polymatroids developed by Lov\u00e1sz $[13]$ to a new abstract system,  which we call  a parity system. Examples of parity systems may be obtained by combining either, two delta-matroids, or two orthogonal 2-polymatroids, on the same ground-sets. We show that many of the results of Lov\u00e1sz concerning 'double flowers' and 'projections' carry over to parity systems.<\/jats:p>","DOI":"10.37236\/1492","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:06:02Z","timestamp":1578708362000},"source":"Crossref","is-referenced-by-count":0,"title":["Parity Systems and the Delta-Matroid Intersection Problem"],"prefix":"10.37236","volume":"7","author":[{"given":"Andr\u00e9","family":"Bouchet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bill","family":"Jackson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1999,9,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:32:30Z","timestamp":1579325550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,9,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1492","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,9,3]]},"article-number":"R14"}}