A subposet Q′ of a poset Q is a copy of a poset P if there is a bijection f between elements of P and Q′ such that x ≤ y in P iff f(x) ≤ f(y) in Q′. For posets P, P ′, let the poset Ramsey number R(P, P ′) be the smallest N such that no matter how the elements of the Boolean lattice QN are colored red and blue, there is a copy of P with all red elements or a copy of P ′ with all blue elements. ...

A comparability graph is a simple graph which admits a transitive orientation on its edges. Each one of such orientations defines a poset on the vertex set, and also it is said that this graph is the comparability graph of the poset. A treelike poset is a poset whose covering graph is a tree. Comparability graphs of arborescence posets are known as trivially perfect graphs. These have been char...

The aim of this paper is to define and study pointed and multi-pointed partition posets of type A and B (in the classification of Coxeter groups). We compute their characteristic polynomials, incidence Hopf algebras and homology groups. As a corollary, we show that some operads are Koszul over Z. Introduction For every finite Weyl group W , there exists a generalized partition poset (cf. [2]) d...

This is an elementary presentation of the arithmetic of trees. We show how it is related to the Tamari poset. In the last part we investigate various ways of realizing this poset as a polytope (associahedron), including one inferred from Tamari’s thesis.

In this paper a system of axioms is presented to define the notion of an experimental system. The primary feature of these axioms is that they are based solely on the mathematical notion of a direct product decomposition of a set. Properties of experimental systems are then developed. This includes defining negation, implication, conjunction, and disjunction on the set 4 of all binary experimen...

We investigate the topology and combinatorics of a topological space called the edge-product space that is generated by the set of edge-weighted finite labelled trees. This space arises by multiplying the weights of edges on paths in trees, and is closely connected to tree-indexed Markov processes in molecular evolutionary biology. In particular, by considering combinatorial properties of the T...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

this work is devoted to give a charcaterization of a pomonoid $s$such that all cyclic $s$-posets are regular injective.

For a positive integer k, let k + k denote the poset consisting of two disjoint k-element chains, with all points of one chain incomparable with all points of the other. Bosek, Krawczyk and Szczypka showed that for each k ≥ 1, there exists a constant ck so that First Fit will use at most ckw 2 chains in partitioning a poset P of width at most w, provided the poset excludes k+k as a subposet. Th...

Let U0, U1 be two normal measures on κ. We say that U0 is in the Mitchell oredering less then U1, U0 ⊳ U1, if U0 ∈ Ult(V, U1). The ordering is wellknown to be transitive and well-founded. It has been an open problem to find a model where ⊳ embeds the four-element poset | |. We find a generic extension where all well-founded posets are embeddable. Hence there is no structural restriction on the ...