The. theory of reduced incidence algebras of binomial posets furnishes a unified treatment of several types of generating functions that arise in enumerative combinatorics. Using this theory as a tool, we study ‘reduced covering algebras’ of binomial lattices and show that they are isomorphic to various algebras of q-binomial generating functions for certain modular binomial lattices.

A hash family is a collection of N functions from a domain of size k to a range of size w. A function ‘separates’ two elements of the domain if it maps them to distinct elements of the range. A perfect hash family of strength t requires that for every set of t elements of the domain, one of the functions separates every pair of the t. A distributing hash family weakens the requirement so that, ...

Software systems generally have a large number of configurable options interacting with each other. Such systems are more likely to be prone to errors, crashes, and faulty executions that are usually caused by option interactions. To avoid such errors, testing all possible configurations during the development phase is usually not feasible, since the number of all possible configurations is exp...

It is known that any k-uniform family with covering number t has at most k t t-covers. In this paper, we give better upper bounds for the number of t-covers in k-uniform intersecting families with covering number t.

Let X be a finite set. We denote by (~) the family of all k-element subsets of X. A family ~satisfying ~ c (~) is called k-uniform. The vertex set of @ is X and it is often denoted by V(Y). An element of ~ is also called an edge of J~. The family ~ is called intersecting if Fc~ G ¢ 25 holds for every F, G ~ ~ . A set C c X is called a cover (or transversal set) of Y if it intersects every edge ...

Today, there are a lot of useful algorithms for covering array (CA) generation, one the branches combinatorial testing. The major CA challenge is generation an with minimum number test cases (efficiency) in appropriate run-time (performance), large systems. strategies classified into several categories: computational and meta-heuristic, to name most important ones. Generally, have high performa...

A generating family in a category C is a collection of objects {Ai|i ∈ I} such that if for any subobject Y // m //X, every Ai f //X factors through m, then m is an isomorphism – i.e. the functors C(Ai, ) are collectively conservative. In this paper, we examine some circumstances under which subobjects of 1 form a generating family. Objects for which subobjects of 1 do form a generating family a...

Combinatorial testing makes it possible to test large systems effectively while maintaining certain coverage guarantees. At the same time, construction of optimized covering arrays (CAs) with a number columns is challenging task. Heuristic and Metaheuristic approaches often become inefficient when applied instances, as computation quality for new moves or solutions during search becomes too slo...