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 Gröbner bases of quadrics with respect to suitable term orders. Since the initial monomials of the elements of these Gröbner bases are square- free, it follows by a result of STURMFELS S, 13.15], that the algebras under consideration are normal, and thus Cohen-Macaulay.