Characterizing Profiles ofk-Families in Additive Macaulay Posets

A subset of a poset is ak-familyif there is no chain consisting ofk+1 of its elements. A subset of a ranked poset consisting ofpi elements of ranki,i=0, 1, ..., Ris said to haveprofilep0,p1, …, pR. A characterization is given for profiles ofk-families in additive Macaulay posets.