Weak-order extensions of an order

✍ Scribed by Karell Bertet; Jens Gustedt; Michel Morvan

• Book ID: 104325800
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 304 KB
• Volume: 304
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(03)00132-4

✦ Synopsis

In this paper, at ÿrst 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.