I took some pictures which are a little similar to our logo picture (last picture below). A lot of interesting developments and ideas in various directions! The polymath picture Polymath 16 of the chromatic number of the plane is in its eleventh post. Here is a subsequent paper about the more general Kahn’s conjecture Our results also apply to the more general setting of matroids.Įarlier the best result was giving disjoint transversal bases. In this paper we prove that one can always find $\left(1/2-o\left(1\right)\right)n$ disjoint transversal bases, improving on the previous best bound of $\Omega\left(n/\log n\right)$. Rota’s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers (for example, the conjecture was recently the subject of the collaborative “Polymath” project). Given $n$ bases $B_$ (we call such bases transversal bases). Halfway to Rota’s basis conjecture, by Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, and Benny SudakovĪbstract: In 1989, Rota made the following conjecture. Three short items: Progress on Rota’s conjecture (polymath12) by Bucić, Kwan, Pokrovskiy, and Sudakovįirst, there is a remarkable development on Rota’s basis conjecture ( Polymath12) described in the paper
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