Pandit, SudipSudipPanditSaha, JoydipJoydipSahaSengupta, IndranathIndranathSengupta2025-08-312025-08-312023-09-0110.1142/S02194988235018522-s2.0-85132991128http://repository.iitgn.ac.in/handle/IITG2025/25743In this paper, we carry out a fairly comprehensive study of two special classes of numerical semigroups, one generated by the sequence of partial sums of an arithmetic progression and the other one generated by a shifted geometric progression, in embedding dimension 4. Both these classes have the common feature that they have unique expansions of the Apéry set elements.falseApéry set | Frobenius number | monomial curves | Numerical semigroups | pseudo-Frobenius number | syzygies | tangent cone | typeArticle1 September 202302350185arJournal0WOS:000849401200003