base


Rota's basis conjecture ★★★

Author(s): Rota

Conjecture   Let $ V $ be a vector space of dimension $ n $ and let $ B_1,\ldots,B_n \subseteq V $ be bases. Then there exist $ n $ disjoint transversals of $ B_1,\ldots,B_n $ each of which is a base.

Keywords: base; latin square; linear algebra; matroid; transversal

Syndicate content