Improved Bounds for Rota's Basis Conjecture

Abstract

We prove that, if B1,...,Bn are disjoint bases of a rank-n matroid, then there are at least \(\frac{n}{{7\log n}}\) disjoint transversals of (B1,...,Bn) that are also bases.

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Correspondence to Sally Dong.

Additional information

This research was partially supported by grants from the Office of Naval Research [N00014-10-1-0851] and NSERC [203110-2011] as well as an Undergraduate Student Research Award from NSERC.

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Dong, S., Geelen, J. Improved Bounds for Rota's Basis Conjecture. Combinatorica 39, 265–272 (2019). https://doi.org/10.1007/s00493-018-3859-1

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Mathematics Subject Classification (2010)

  • 05B35