Log-concavity and compressed ideals in certain Macaulay posets Original Research Article

Let Bn be the poset of subsets of {1,2,…,n} ordered by inclusion and Mn be the poset of monomials in x1,x2,…,xn ordered by divisibility. Both these posets have an additional linear order making them what is called Macaulay posets. We show in this paper that the profiles (also called f-vectors) of ideals in Bn and Mn generated by the first elements (relatively to the linear order) of a given rank are log-concave.