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Comparability Invariance Results for Tolerance Orders
by
Ann N Trenk
Wellesley College
Coauthors: Kenneth P Bogart (Dartmouth College), Garth Isaak (Lehigh University), Joshua D Laison (Dartmouth College)
A property or parameter of a ordered set is said to be comparability invariant if all orders with a given comparability graph have that property or have the same value of that parameter. A well-known example is dimension - any two orders with the same comparability graph have the same dimension.
In this talk we discuss comparability invariance results for three classes which are generalizations of interval orders. An order P = (V, \prec) is a bounded tolerance order if each v in V can be assigned a real interval Iv and a real number tolerance 0 < tv <= |Iv| so that x \prec y if and only if center(Ix) < center(Iy) and |Ix \cap Iy| < min{tx, ty}. We prove that membership in the class of bounded tolerance orders (and two other related classes) is comparability invariant.
Date received: April 18, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cags-30.