Reduction of Rota's Basis Conjecture to a Problem on Three Bases

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Previous article Next article Reduction of Rota's Basis Conjecture to a Problem on Three BasesTimothy Y. ChowTimothy Y. Chowhttps://doi.org/10.1137/080723727PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that Rota's basis conjecture follows from a similar conjecture that involves just three bases instead of n bases.[1] R. Aharoni and and E. Berger, The intersection of a matroid and a simplicial complex, Trans. Amer. Math. Soc., 358 (2006), pp. 4895–4917. TAMTAM 0002-9947 CrossrefISIGoogle Scholar[2] W. Chan, An exchange property of matroid, Discrete Math., 146 (1995), pp. 299–302. DSMHA4 0012-365X CrossrefISIGoogle Scholar[3] T. Chow, On the Dinitz conjecture and related conjectures, Discrete Math., 145 (1995), pp. 73–82. DSMHA4 0012-365X CrossrefISIGoogle Scholar[4] A. A. Drisko, On the number of even and odd Latin squares of order $p+1$, Adv. Math., 128 (1997), pp. 20–35. ADMTA4 0001-8708 CrossrefISIGoogle Scholar[5] Google Scholar[6] J. Geelen and and P. J. Humphries, Rota's basis conjecture for paving matroids, SIAM J. Discrete Math., 20 (2006), pp. 1042–1045. 0895-4801 LinkISIGoogle Scholar[7] J. Geelen and and K. Webb, On Rota's basis conjecture, SIAM J. Discrete Math., 21 (2007), pp. 802–804. 0895-4801 LinkISIGoogle Scholar[8] R. Huang and and G.-C. Rota, On the relations of various conjectures on Latin squares and straightening coefficients, Discrete Math., 128 (1994), pp. 225–236. DSMHA4 0012-365X CrossrefISIGoogle Scholar[9] Google Scholar[10] J. Keijsper,An algorithm for packing connectors, J. Combin. Theory Ser. B, 74 (1998), pp. 397–404. JCBTB8 0095-8956 CrossrefISIGoogle Scholar[11] Google Scholar[12] V. Ponomarenko, Reduction of jump systems, Houston J. Math., 30 (2004), pp. 27–33. HJMADZ 0362-1588 ISIGoogle Scholar[13] D. Mayhew and and G. F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B, 98 (2008), pp. 415–431. JCBTB8 0095-8956 CrossrefISIGoogle Scholar[14] M. Wild, On Rota's problem about n bases in a rank n matroid, Adv. Math., 108 (1994), pp. 336–345. ADMTA4 0001-8708 CrossrefISIGoogle Scholar[15] P. Zappa, The Cayley determinant of the determinant tensor and the Alon–Tarsi conjecture, Adv. in Appl. Math., 19 (1997), pp. 31–44. 0196-8858 CrossrefISIGoogle ScholarKeywordscommon independent setsnon–base-orderable matroidodd wheel Previous article Next article FiguresRelatedReferencesCited byDetails Complexity of packing common bases in matroids8 April 2020 | Mathematical Programming, Vol. 188, No. 1 Cross Ref Determinants, choices and combinatoricsDiscrete Mathematics, Vol. 342, No. 1 Cross Ref On Disjoint Common Bases in Two Matroids15 December 2011 | SIAM Journal on Discrete Mathematics, Vol. 25, No. 4AbstractPDF (347 KB)The Conjectures of Alon–Tarsi and Rota in Dimension Prime Minus One14 April 2010 | SIAM Journal on Discrete Mathematics, Vol. 24, No. 2AbstractPDF (138 KB) Volume 23, Issue 1| 2009SIAM Journal on Discrete Mathematics History Submitted:08 May 2008Accepted:29 September 2008Published online:07 January 2009 InformationCopyright © 2009 Society for Industrial and Applied MathematicsKeywordscommon independent setsnon–base-orderable matroidodd wheelMSC codes05B2015A03PDF Download Article & Publication DataArticle DOI:10.1137/080723727Article page range:pp. 369-371ISSN (print):0895-4801ISSN (online):1095-7146Publisher:Society for Industrial and Applied Mathematics