The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing structural, characterizing, and enumerative properties.

With a nite graph G V E we associate a partially ordered set P X P with X V E and x e in P if and only if x is an endpoint of e in G This poset is called the incidence poset of G In this paper we consider the function M p d de ned for p d as the maximum number of edges a graph G can have when it has p vertices and the dimension of its incidence poset is at most d It is easy to see that M p p as...

In recent years, researchers have shown renewed interest in combinatorial properties of posets determined by geometric properties of its order diagram and topological properties of its cover graph. In most cases, the roots for the problems being studied today can be traced back to the 1970’s, and sometimes even earlier. In this paper, we study the problem of bounding the dimension of a planar p...

We give a new order-theoretic characterization of a complete Heyting and co-Heyting algebra C. This result provides an unexpected relationship with the field of Nash equilibria, being based on the so-called Veinott ordering relation on subcomplete sublattices of C, which is crucially used in Topkis’ theorem for studying the order-theoretic stucture of Nash equilibria of supermodular games. Intr...

This work-in-progress is intended as an exposition of the background material, results, and open problems of a particular poset theoretic study of Weyl characters and semisimple Lie algebra representations begun in the late 1970’s and early 1980’s in the work of Richard P. Stanley and Robert A. Proctor.

In this paper all poset structures are classi£ed which admit the MacWilliams identity, and the MacWilliams identities for poset weight enumerators corresponding to such posets are derived. We prove that being a hierarchical poset is a necessary and suf£cient condition for a poset to admit MacWilliams identity. An explicit relation is also derived between P-weight distribution of a hierarchical ...

Let R be a non empty poset and let A, B be many sorted sets indexed by R. One can check that every many sorted relation between A and B which is os-compatible is also order-sorted. Let R be a non empty poset and let A be a many sorted set indexed by the carrier of R. An order sorted relation of A is an order sorted relation of A, A. Let S be an order sorted signature and let U1 be an order sort...