Toric rings generated by special stable sets of monomials

In this paper we consider some subalgebras of the d-th Veronese subring of a polynomial ring, generated by stable subsets of monomials. We prove that these algebras are Koszul, showing that the presentation ideals have Grobne r bases of quadrics with respect to suitable term orders. Since the initial monomials of the elements of these Grobner bases are square- free, it foll ows by a result of STURMFELS [S, 13.15], that the algebras under considerat ion are normal, and thus Cohen-Macaulay.