Smallest known formula for the determinant The smallest known formula for the determinant has size $n^{\mathcal O(\log n)}$ according to the folklore (or to Ran Raz in its paper Multi-Linear Formulas for Permanent and Determinant are of Super-Polynomial Size). 

Do you have any reference for this? In particular, what is this formula?
One way is described in Berkowitz, On computing the determinant in small parallel time using a small number of processors (see also Soltys, Berkowitz's algorithm and clow sequences). Another way is described in Hrubeš and Tzameret, Short proofs for the determinant identities.