There are multiple ways to parenthesize a sequence of factors two at a time For instance and can be grouped as either or ; the Catalan numbers count the number of ways this is possible for factors The groupings form a partially ordered set where one grouping covers another if the first can be transformed into the second by taking a subelement of the form and replacing it with In these transformations and can be a single factor or a product of factors These partially ordered sets form a lattice called the Tamari lattice This Demonstration shows graphs formed by lattices generated from factor sequences of different lengths where each vertex label is a polygon triangulation corresponding to a particular grouping of factors