# Rota, Gian-Carlo

## Rota's basis conjecture ★★★

Author(s): Rota

**Conjecture**Let be a vector space of dimension and let be bases. Then there exist disjoint transversals of each of which is a base.

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

## Rota's unimodal conjecture ★★★

Author(s): Rota

Let be a matroid of rank , and for let be the number of closed sets of rank .

**Conjecture**is unimodal.

**Conjecture**is log-concave.

Keywords: flat; log-concave; matroid