{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814001,"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>Given any system of $n$ subsets in a matroid $M$, a transversal of this system is an $n$-tuple of elements of $M$, one from each set, which is independent. Two transversals differing by exactly one element are adjacent, and two transversals connected by a sequence of adjacencies are locally equivalent, the distance between them being the minimum  number of adjacencies in such a sequence.  We give two sufficient conditions for all transversals of a set system  to be locally equivalent. Also we propose a conjecture that the distance  between any two locally equivalent transversals can be bounded by a function  of $n$ only, and provide an example showing that such function,  if it exists, must grow at least exponentially.<\/jats:p>","DOI":"10.37236\/1248","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:26:16Z","timestamp":1578687976000},"source":"Crossref","is-referenced-by-count":0,"title":["Local equivalence of transversals in matroids"],"prefix":"10.37236","volume":"3","author":[{"given":"D.","family":"Fon-Der-Flaass","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,8,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T01:17:06Z","timestamp":1579310226000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,8,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1248","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1996,8,2]]},"article-number":"R24"}}