Abstract
A class of finite partially ordered sets isinvertible if the inverse (dual) of every poset in the class is in the class, and iszero-augmentable if the addition of a new element below all others yields a poset in the class for each member. This paper demonstrates that certain classes of posets that have representations byN-gons in the plane ordered by proper inclusion are neither invertible nor zero-augmentable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Dushnik and E. W. Miller (1941) Partially ordered sets,Amer. J. Math. 63, 600–610.
P. C. Fishburn (1988) Interval orders and circle orders,Order 5, 225–234.
P. C. Fishburn (1989) Circle orders and angle orders,Order 6, 39–47.
P. C. Fishburn and W. T. Trotter (1985) Angle orders,Order 1, 333–343.
P. C. Fishburn and W. T. Trotter (1988) Angle orders and zeros, AT&T Bell Laboratories, Murray Hill, NJ.
R. L. Graham, B. L. Rothschild, and J. H. Spencer (1980)Ramsey Theory, Wiley, New York.
N. Santoro and J. Urrutia (1987) Angle orders, regularn-gon orders and the crossing number,Order 4, 209–220.
J. B. Sidney, S. J. Sidney, and J. Urrutia (1988) Circle orders,n-gon orders and the crossing number of partial orders,Order 5, 1–10.
J. Urrutia (1988) Partial orders and Euclidean geometry, inAlgorithms and Order (ed. I. Rival), Kluwer Academic Pubs., Dordrecht, pp. 387–434.
Author information
Authors and Affiliations
Additional information
Communicated by I. Rival
AMS subject classification (1980). 06A10.
Rights and permissions
About this article
Cite this article
Fishburn, P.C. On invertibility and zero-augmentability ofN-gon orders. Order 6, 159–173 (1989). https://doi.org/10.1007/BF02034333
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02034333