We introduce and study the notion of read- k projections of the determinant: a polynomial f F [ x 1 x n ] is called a {\it read- k projection of determinant} if f = d et ( M ) , where entries of matrix M are either field elements or variables such that each variable appears at most k times in M . A monomial set S is said to be expressible as read- k projection of determinant if there is a read- k projection of determinant f such that the monomial set of f is equal to S . We obtain basic results relating read- k determinantal projections to the well-studied notion of determinantal complexity. We show that for sufficiently large n , the n n permanent polynomial Per m n and the elementary symmetric polynomials of degree d on n variables S n d for 2 d n − 2 are not expressible as read-once projection of determinant, whereas mon ( Per m n ) and mon ( S n d ) are expressible as read-once projections of determinant. We also give examples of monomial sets which are not expressible as read-once projections of determinant.