“…d as d grows to +∞, where q p,n > 0. Moreover, it has been proved in [2] that the roots of the limit face polynomial q ∞ n (T ) = n p=0 q p,n T p are all simple and real in [−1, 0], and in [3] that this polynomial is symmetric with respect to the involution T → −T − 1, see Theorem 11. We first observe that this symmetry actually follows from a general symmetry phenomenon obtained by I. G. Macdonald in [6] which can be formulated as follows, see Theorem 8.…”