# Rota's conjecture

The objective of this Polymath project is to prove

Rota's conjecture: if $B_1,\dots,B_n$ are $n$ bases of an $n$-dimensional vector space $V$ (not necessarily distinct or disjoint), then there exists an $n \times n$ grid of vectors $(v_{ij})$ such that
1. the $n$ vectors in row $i$ are the members of the $i^{th}$ basis $B_i$ (in some order), and
2. in each column of the matrix, the n vectors in that column form a basis of V.

## References

• [HKL2010] On disjoint common bases in two matroids, Nicholas J. A. Harvey, Tam´as Kir´aly, and Lap Chi Lau, TR-2010-10. Published by the Egerv´ary Research Group, P´azm´any P. s´et´any 1/C, H–1117, Budapest, Hungary.