A weak version of Rota's basis conjecture for odd dimensions

Abstract

The Alon-Tarsi Latin square conjecture is extended to odd dimensions by stating it for reduced Latin squares (Latin squares having the identity permutation as their first row and first column). A modified version of Onn's colorful determinantal identity is used to show how the validity of this conjecture implies a weak version of Rota's basis conjecture for odd dimensions, namely that a set of $n$ bases in ${\mathbb{R}}^n$ has $n-1$ disjoint independent transversals.

Cited by in corpus (1)

• On extensions of the Alon-Tarsi Latin Square conjecture