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A forbidden-suborder characterization of binarily-composable diagrams in double categories

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Robert Dawson

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.

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