Minimal free resolution of generalized repunit algebras

Let k be an arbitrary field and let b>1, n>1 and a be three positive integers. In this paper we explicitly describe a minimal S-graded free resolution of the semigroup algebra kS when S is a generalized repunit numerical semigroup, that is, when S is the submonoid of N generated by a1, a2, …, an where a1=∑j=0n−1bj and ai−ai−1=a bi−2, i=2, …, n, with gcd (a, a1) =1.