2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102148There is a familiar conjugate for integer partitions: transpose the Ferrers diagram, and a conjugate for integer compositions: transpose a Ferrers-like diagram. Here we propose a conjugate for set partitions and show that it interchanges # singletons and # adjacencies. Its restriction to noncrossing partitions cropped up in a 1972 paper of Kreweras. We also exhibit an analogous pairs of statistics interchanged by the composition conjugate.Improved definition of conjugate partition; noncrossing partitions considered. 7 pagesCombinatorics05A18; 05A17text