ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS

On the covering of pairs by quadruples

Covering and packing for pairs

a Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore b Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ 85287-8809, USA c Department of Computer Science, University of Vermont, Burlington, VT 05405, USA d Department of Mathematics, 253-37, Cal...

Sequence Covering Arrays and Linear Extensions

Covering subsequences by sets of permutations arises in numerous applications. Given a set of permutations that cover a specific set of subsequences, it is of interest not just to know how few permutations can be used, but also to find a set of size equal to or close to the minimum. These permutation construction problems have proved to be computationally challenging; few explicit constructions...

On integral bases in relative quadratic extensions

Let F be an algebraic number field and E a quadratic extension with E = F(√μ). We describe a minimal set of elements for generating the integral elements oE of E as an oF module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of E as well. In the last section, we present examples of...

On the Number of Covering Pairs in Speciied Lattices

Given a class F of posets, let ex(F; n) denote the maximum number of covering pairs achieved by an n-element poset in F. We determine this number for the class of N-free lattices and give crude lower and upper bounds for the classes of distributive and covering lattices. The structural characterization of covering lattices leads us to a class of lattices whose elements have a bounded number of ...

Covering Pairs in Directed Acyclic Graphs

The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In this paper, we study the computational complexity of two constrained variants of Minimum Path Cover motivated by the recent introduction of next-generation ...