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 k[S] 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.