Matchings, cutsets, and chain partitions in graded posets
The author collects and introduces several properties of graded posets (cutset property, strong cutset property, skipless Dilworth property, LYM property, matching property, strong matching property, nested chain property, normalized matching property, rank-symmetric, rank-unimodal, Sperner property, strong Sperner property, chain property). He determines implications among these properties with the exception of one long- standing conjecture of the author about LYM posets. Examples of posets realizing the possible combinations of properties are presented.
scientific article; zbMATH DE number 797071
scientific article