Tilings of rectangles with rectangles, and tileorders (the associated double order structures) are useful as ``templates'' for composition in double categories. In this context, it is particularly relevant to ask which tilings may be joined together, two rectangles at a time, to form one large rectangle. We characterize such tilings via forbidden suborders, in a manner analogous to Kuratowski's characterization of planar graphs.
Keywords: Double categories, tileorders, binary composition, Hasse diagrams, forbidden suborders.
AMS Classification (1991): 18D05, 05B45.
Theory and Applications of Categories, Vol. 1, 1995, No. 7, pp 146-153.