On a conjecture of Erdös and Rényl

We show that for A ranging over n×n circulants with three ones in each row, where n is prime, $\text{lim inf}\text{|}\text{det}\text{A|}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{>1}$. For a subfamily containing almost all A's this lim inf is in fact 1.38…. We also compute the permanents of a certain family of matrices.