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Planar Lattices

Published online by Cambridge University Press:  20 November 2018

David Kelly  and
Ivan Rival
David Kelly
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Ivan Rival
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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A finite partially ordered set (poset) P is customarily represented by drawing a small circle for each point, with a lower than b whenever a < b in P, and drawing a straight line segment from a to b whenever a is covered by b in P (see, for example, G. Birkhoff [2, p. 4]). A poset P is planar if such a diagram can be drawn for P in which none of the straight line segments intersect.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 636 - 665
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Baker, K. A., Fishburn, P. C., and Roberts, F. S., Partial orders of dimension 2, Networks 2 (1971), 11–28.Google Scholar
2. Birkhoff, G., Lattice theory, 3rd. ed. (American Mathematical Society, Providence, R.I. 1967).Google Scholar
3. Dushnik, B. and Miller, E. W., Partially ordered sets, Amer. J. Math. 63 (1941), 600–610.Google Scholar
4. Grâtzer, G., Lattice theory: first concepts and distributive lattices (W. H. Freeman, San Francisco, 1971).Google Scholar
5. Kelly, D., Planar partially ordered sets (preprint, 1973).Google Scholar
6. Kelly, D. and Rival, I., Crowns, fences and dismantlable lattices, Can. J. Math. 26 (1974), 1257–1271.Google Scholar
7. Kuratowski, K., Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271–283.Google Scholar
8. Piatt, C. R., Planar lattices and planar graphs, J. Combinatorial Theory Ser. B (to appear).Google Scholar
9. Rival, I., Lattices with doubly irreducible elements, Can. Math. Bull. 17 (1974), 91–95.Google Scholar
10. Wille, R., On modular lattices of order dimension two, Proc. Amer. Math. Soc. 43 (1974), 287–292.Google Scholar