Abstract
Our objective is to draw order diagrams without edge crossings, on surfaces. We establish several fundamental results about the genus of orders and apply these to certain familiar orders. For instance, every lattice contains an irreducible element of degree at most 4 genus + 3.
These results are driven by the continuing interest in drawing and reading order diagrams. Work on these is also motivated by the attention recently drawn to order as a model for motion planning — even in such particularly Canadian contexts as ice flow analysis and this, in turn has cast new light on such old and fundamental problems as diagram invariance.
The work reported here was done during this author's visit to the University of Ottawa.
This work was supported by the Natural Sciences and Engineering Research Council of Canada.
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© 1991 Springer-Verlag Berlin Heidelberg
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Reuter, K., Rival, I. (1991). Genus of orders and lattices. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1990. Lecture Notes in Computer Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53832-1_48
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DOI: https://doi.org/10.1007/3-540-53832-1_48
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