A poset is called upper homogeneous (or "upho") if every principal order filter of the isomorphic to whole poset. We observe that rank and characteristic generating functions upho posets are multiplicative inverses one another.

We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We will prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving partitions) of a finite n-element poset P with n ≥ 3 is homotopy equivalent to a wedge of spheres of dimension n − 3. If P is connected, then the number of spheres is...

The Bruhat order gives a poset structure to any Coxeter group. The ideal of elements in this poset having boolean principal order ideals forms a simplicial poset. This simplicial poset defines the boolean complex for the group. In a Coxeter system of rank n, we show that the boolean complex is homotopy equivalent to a wedge of (n− 1)-dimensional spheres. The number of these spheres is the boole...

A graph G s = (V , E s) is a sandwich for a pair of graphs G t = (V , E t) and G = (V , E) if E t ⊆ E s ⊆ E. A sandwich problem asks for the existence of a sandwich graph having an expected property. In a seminal paper, Golumbic et al. [Graph sandwich problems, J. Algorithms 19 (1995) 449–473] present many results on sub-families of perfect graphs. We are especially interested in comparability ...

Let (W,S) be a finite Weyl group and let w ∈ W . It is widely appreciated that the descent set D(w) = {s ∈ S | l(ws) < l(w)} determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results to the situation of the Bruhat poset W J where J ⊂ S. Our main results here include the identification of a certain subset S ⊂ W J that convinci...

This paper continues a recent resurgence of interest in combinatorial properties of a poset that are associated with graph properties of its cover graph and order diagram. The following two theorems appearing in a 1977 paper of Trotter and Moore have played important roles in motivating this more modern research: (1) The dimension of a poset is at most 3 when its cover graph is at tree; (2) The...

this paper is devoted to the study of products of classes of right $s$-posets possessing one of the flatness properties and preservation of such properties under products. specifically, we characterize a pomonoid $s$ over which its nonempty products as right $s$-posets satisfy some known flatness properties. generalizing this results, we investigate products of right $s$-posets satisfying condi...

We discuss some properties of a subposet of the Tamari lattice introduced by Pallo (1986), which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial...

In this paper x denotes a set and R denotes a non empty poset. Next we state two propositions: (1) For all order sorted sets X, Y of R holds X ∩Y is an order sorted set of R. (2) For all order sorted sets X, Y of R holds X ∪Y is an order sorted set of R. Let R be a non empty poset and let M be an order sorted set of R. A many sorted subset indexed by M is said to be an order sorted subset of M ...

We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of S we also present conditions on the poset A that are necessary and s...