Theorems on intervals of ordered sets

Some Representation Theorems for Partially Ordered Sets

Ordering Subsets of (partially) Ordered Sets: Representation Theorems

In many practical situations, we have a (partially) ordered set V of different values. For example, we may have the set of all possible values of temperature, or the set of all possible degrees of confidence in a statement. In practice, we are often uncertain about the exact value of the quantity. Due to this uncertainty, at best, we know a set S ⊆ V of possible values of the quantity: e.g., an...

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Some intersection theorems for ordered sets and graphs

Of particular interest are those B for which the maximum families consist of socalled “kernel systems,” i.e., the family of all supersets of some fixed set in B. For example, we show that the set of all (cyclic) translates of a block of consecutive integers in [n] is such a family. It turns out rather unexpectedly that many of the results we obtain here depend strongly on properties of the well...

Chain Decomposition Theorems for Ordered Sets and Other Musings

A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can be partitioned into chains in a “strong” way, is proved. The result is motivated by a conjecture of Graham’s concerning probability correlation inequalities...