részfaktoriális

Részfaktoriális, also known as partial factorial, is a term used in combinatorial mathematics. It refers to a specific subset of all possible factorial arrangements of a set of items. In standard factorial calculations, n! represents the total number of ways to arrange n distinct items in a sequence. Részfaktoriális, however, considers only a selection of these arrangements based on certain criteria or constraints.

The concept is often employed in experimental design, particularly in fractional factorial designs. These designs are used to study the effects of multiple factors in an experiment efficiently. Instead of testing every single combination of factor levels (which can become prohibitively large), a fractional factorial design selects a carefully chosen subset of these combinations. This subset, the "részfaktoriális," is designed so that estimates of the main effects and some lower-order interactions can still be obtained, albeit with some confounding.

The selection of which combinations to include in a részfaktoriális is not arbitrary. It follows specific aliasing patterns or resolution levels, which determine how the effects of different factors are mixed. A higher resolution design generally allows for clearer estimation of effects with less confounding. The term itself is Hungarian, translating directly to "partial factorial." Its application is crucial in situations where resources, time, or cost limit the possibility of conducting a full factorial experiment.