ABSTRACT
We begin by defining what we mean by a discrete structure. For positive
integer k, a k-ary relation R on a set X is a subset of Xk = {(x1, . . . , xk)} : xi ∈ X for all i}; k is called the arity of R. A discrete structure D on a set V (called the (underlying) vertex set) is (V, {Ri}i∈I), where I is any index set and each Ri is an ni-ary relation on V , for some positive integer ni
(if there is just one relation, we often omit the surrounding set brackets). We
often write (x1, . . . , xk) ∈ D if (x1, . . . , xk) ∈ Ri for some i. Our definition allows for infinite discrete structures (when V is infinite), but unless otherwise
stated, we assume a structure is finite.
