  We introduce a squarefree monomial ideal associated to the set of domino
tilings of a $2\times n$ rectangle and proceed to study the associated minimal
free resolution. In this paper, we use results of Dalili and Kummini to show
that the Betti numbers of the ideal are independent of the underlying
characteristic of the field, and apply a natural splitting to explicitly
determine the projective dimension and Castelnuovo-Mumford regularity of the
ideal.
