On Row-Factorization relations of certain numerical semigroups

Abstract

Let $H$ be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a description of a possible row-factorization $(\RF)$ matrix for each pseudo-Frobenius element of $H.$ Further, when $H$ is symmetric and has embedding dimension 4 or 5, we prove that the defining ideal is minimally generated by $\RF$-relations.