a complete graph on n vertices, the order dimension of the incidence poset is . It follows that all simple n-vertex graphs have incidence posets with order dimension . k-dimension and 2-dimension A generalization of dimension is the notion of k-dimension (written ) which is the minimal number of chains of length at most k in whose product the partial order can be embedded. In particular, the 2-dimension of an order can be seen as the size of the smallest set such that the order embeds in the inclusion order on this set. See also Interval dimension References . . . . . . . . . Order theory Dimension theory