Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of cd-index, long studied in the context of convex polytopes and Eulerian posets, arises as the dual basis to a natural basis of peak quasisymmetric functions introduced by Stembridge. Thus E...

Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of L-domains, has been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embedding-projection pairs to local...

Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that principal order filter at every vertex is isomorphic to whole poset. Well-known examples include k-ary trees, grid graphs, and Stern Very little known about upho in general. In this paper, we construct Schur-positive Ehrenborg quasisymmetric functions, whose rank-generating functions h...

We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to exchangeable random infinite posets.