2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77028We show that the poset of shuffles introduced by Greene in 1988 is flag-symmetric, and we describe a "local" permutation action of the symmetric group on the maximal chains which is closely related to the flag symmetric function of the poset. A key tool is provided by a new labeling of the maximal chains of a poset of shuffles, which is also used to give bijective proofs of enumerative properties originally obtained by Greene. In addition we define a monoid of multiplicative functions on all posets of shuffles and describe this monoid in terms of a new operation on power series in two variables.34 pages, 6 figuresCombinatorics05A15 (Primary) 05E05, 05E25 (Secondary)text