Weak-order extensions of an order

Authors:
Karell Bertet;Jens Gustedt;Michel Morvan
Affiliations:
L3I, Université de La Rochelle, Pôle Sciences et Technologie, Av Michel Crépeau, 17042 La Rochelle, Cédex 1, France;LORIA and INRIA, campus scientifique, BP 239, F-54506 Vandoeuvre-lès-Nancy, France;LIAFA - Université Denis Diderot Paris 7, Case 7014 - 2, place Jussieu, 75256 Paris, Cedex 05, France
Venue:
Theoretical Computer Science
Year:
2003

Citing 3
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Weak-Order Extensions of an Order

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Abstract

In this paper, at first we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.