A simple proof of Suzumura's extension theorem for finite domains with applications. Issue 3 (2002)

• Record Type: Journal Article
• Authors: Lahiri, Somdeb
• Is Part Of: Journal of applied mathematics & decision sciences. Volume 6:Issue 3(2002)
• Page Start: 183
• Page End: 190
• Publication Date: 2002
• Subjects: Operations research -- Periodicals; Mathematical models -- Periodicals; Statistics -- Periodicals; Quality control -- Periodicals; Mathematical models; Operations research; Quality control; Statistics; Periodicals; 519.05
• DOI: 10.1155/S1173912602000111
• Languages: English
• ISSNs: 1173-9126

Abstract

Abstract : In this paper we provide a simple proof of the extension theorem for partial orderings due to Suzumura [1983] when the domain of the partial order is finite. The extension theorem due to Szpilrajn [1930] follows from this theorem. Szpilrajns extension theorem is used to show that an asymmetric binary relation is contained in the asymmetric part of a linear order if and only if it is acyclic. This theorem is then applied to prove three results. Finally we introduce the concept of a threshold choice function, and our third result says that such choice functions are the only ones to satisfy a property called functional acyclicity.