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

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.

http://www.tac.mta.ca/tac/volumes/1995/n7/v1n7.dvi
http://www.tac.mta.ca/tac/volumes/1995/n7/v1n7.ps
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n7/v1n7.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n7/v1n7.ps

TAC Home