Partial orders have applications in various areas in computer science such as distributed systems, object oriented languages, knowledge representation systems and databases. In this paper we present a new technique to encode partially ordered sets or posets. Specifically, we use the family of two-dimensional posets, which we refer to as rectangles, to encode a given poset; an element x is less ...

In this paper, we first find the set of orders of all elements in some special linear groups over the binary field. Then, we will prove the characterizability of the special linear group PSL(13, 2) using only the set of its element orders.

We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing efficiently near-optimal search strategies for typical partial orders. We consider two classical models for random partial orders, the random graph model and the uniform model. We shall show that certain simple, fast algorithms are able to produce nearly-optim...

We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparision is made w...

A boolean term order is a total order on subsets of [n] = {1,. .. , n} such that ∅ ≺ α for all α ⊆ [n], α = ∅, and α ≺ β ⇒ α ∪ γ ≺ β ∪ γ for all γ with γ ∩ (α ∪ β) = ∅. Boolean term orders arise in several different areas of mathematics, including Gröbner basis theory for the exterior algebra, and comparative probability. The main result of this paper is that boolean term orders correspond to o...