2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58736Using a new graphical representation for partitions, the author obtains a family of partition identities associated with partitions into distinct parts of an arithmetic progression, or, more generally, with partitions into distinct parts of a set that is a finite union of arithmetic progressions associated with a modular sum-free Sidon set. Partition identities are also constructed for sets associated with modular sum-free sets.9 pages. To appear in The Ramanujan JournalNumber TheoryCombinatoricsPrimary 11P81, 11P83. Secondary 11B05, 11B25, 11B75text