Cayleylike

Cayleylike is an adjective used in mathematics to describe objects, structures, or methods that resemble aspects of Arthur Cayley's work in algebra, particularly the representation of algebraic structures via generators and relations and the use of graph-theoretic constructions to encode group actions. In practice, a construction is described as Cayleylike when it can be framed by a finite generating set together with a set of relations that govern how the generators interact, enabling systematic generation of elements or states by successive applications of the generators.

Key features often associated with Cayleylike constructions include regularity or vertex transitivity, a high degree of symmetry, and a natural state space that admits a labeled graph representation in which edges correspond to generator actions. This perspective emphasizes constructive describability: an object is Cayleylike if one can traverse or build it by applying a known set of moves.

Common examples cited as Cayleylike are Cayley graphs themselves, such as cycle graphs C_n and hypercubes Q_n, which arise from the cyclic group Z_n and the vector space (Z_2)^n, respectively. In broader use, Cayleylike terminology appears in discussions of interconnection networks, algebraic coding, and computational group theory as a way to categorize structures that share Cayley-style generation and symmetry.

Notes: the term is informal and context-dependent; it is not a standard technical designation in all subfields. See also Cayley graph, group theory, and algebraic graph theory.