Generants
Generants are a concept in abstract algebra and related fields used to describe a seed set that, under a prescribed generation rule, yields a given structure. A generant may be a single element or a finite subset G of a structure S equipped with a generation relation R. The generation process is defined by repeatedly applying R to elements of G to produce new elements, with the closure of G under R denoting the smallest substructure of S containing G and closed under R. A set G is called a generant of S if this closure equals S.
Examples of generants arise when the generation rule R mirrors the operation or rules used to construct
Relation to generators: Generants generalize the standard notion of generators by allowing generation through rules beyond
Applications and status: The term is used in exploratory research to compare generation mechanisms across different