Matchings, cutsets, and chain partitions in graded posets Original Research Article

New properties that involve matchings, cutsets, or skipless chain partitions in graded posets are introduced and compared to familiar Sperner and chain partition properties. Related work is surveyed. We determine all possible combinations of these properties, with the exception of a long-standing open conjecture about LYM posets, and provide a list of examples realizing these combinations.