An online version of Rota's basis conjecture
Combinatorics
2017-10-10 v3
Abstract
Rota's basis conjecture states that in any square array of vectors whose rows are bases of a fixed vector space the vectors can be rearranged within their rows in such a way that afterwards not only the rows are bases, but also the columns. We discuss an online version of this conjecture, in which the permutation used for rearranging the vectors in a given row must be determined without knowledge of the vectors further down the array. The paper contains surprises both for those who believe this online basis conjecture at first glance, and for those who disbelieve it.
Keywords
Cite
@article{arxiv.1312.5953,
title = {An online version of Rota's basis conjecture},
author = {Guus P. Bollen and Jan Draisma},
journal= {arXiv preprint arXiv:1312.5953},
year = {2017}
}
Comments
several further edits, added another reference, final version, to appear in J Alg Comb