{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T00:36:26Z","timestamp":1787358986546,"version":"build-2736575974"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Migal-Tel-Hai"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We show that given two bases $A$ and $B$ of a matroid $\\mathcal M$ and any given partition $\\bigcup_{i=1}^kB_i$ of $B$ there exists a partition $\\bigcup_{i=1}^kA_i$ of $A$ such that $(A- A_i)\\cup B_i$ and $(A- \\bigcup_{j=1}^i A_j)\\cup (\\bigcup_{j=1}^i B_j)$ are bases for all $i=1,\\ldots,k$. We also give a new proof, not relying on Hall's theorem, of a theorem of Donald and Tobey stating that for each $k=1,\\dots,n$, there exists a bijection $\\tau_k$ from $k$-subsets $I$ of $A$ to $k$-subsets of $B$ such that $(A- I)\\cup\\tau_k(I)$ is always a basis.<\/jats:p>","DOI":"10.1137\/19m1291261","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T10:50:34Z","timestamp":1634640634000},"page":"2517-2519","source":"Crossref","is-referenced-by-count":2,"title":["On Sequential Basis Exchange in Matroids"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2662-042X","authenticated-orcid":true,"given":"Dani","family":"Kotlar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elad","family":"Roda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ran","family":"Ziv","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2011.05.006"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/S000497270004140X"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90064-2"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01303201"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700028938"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090303"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580672"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1973-0311494-8"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/0129045"},{"key":"atypb10","first-page":"89","author":"Kajitani Y.","year":"1983","journal-title":"CAS83"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90209-9"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/120867603"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21675"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"J. P. S. Kung,\n                      Basis-exchange properties\n                      , in Theory of Matroids, Encyclopedia Math. Appl. 26, Cambridge University Press, Cambridge, UK, 1986, pp. 62-75.","DOI":"10.1017\/CBO9780511629563.007"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.08.004"},{"key":"atypb16","unstructured":"D. Welsh,\n                      Matroid Theory\n                      , Academic Press, London, 1976."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1291261","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:06:28Z","timestamp":1787317588000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1291261"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1291261"],"URL":"https:\/\/doi.org\/10.1137\/19m1291261","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}