We introduce a new class of admissible pairs of triangular sequences and prove  a bijection between the set of admissible pairs of triangular sequences of length n  and the set of parking functions of length n. For all u and v = 0; 1; 2; 3 and all  n  7 we describe in terms of admissible pairs the dimensions of the bi-graded components   h u;v of diagonal harmonics C [x 1 ; : : : ; x n ; y 1 ; : : : ; y n ]=S n , i.e., polynomials in  two groups of n variables modulo the diagonal action of symmetric group S n 

Michael Shapiro