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We introduce a squarefree monomial ideal associated to the set of dominotilings of a $2\times n$ rectangle and proceed to study the associated minimalfree resolution. In this paper, we use results of Dalili and Kummini to showthat the Betti numbers of the ideal are independent of the underlyingcharacteristic of the field, and apply a natural splitting to explicitlydetermine the projective dimension and Castelnuovo-Mumford regularity of theideal.

Minimal Free Resolutions of $2\times n$ Domino Tilings