✦ LIBER ✦

Well-graded families of relations

✍ Scribed by Jean-Paul Doignon; Jean-Claude Falmagne

Book ID: 104113676
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 471 KB
Volume: 173
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00095-7

No coin nor oath required. For personal study only.

✦ Synopsis

Any semiorder on a finite set can be reached from any other semiorder on the same set by elementary steps consisting either in the addition or in the removal of a single ordered pair, in such a way that only semiorders are generated at every step, and also that the number of steps equals the distance between the two semiorders. Similar results are also established for other families of relations (partial orders, biorders, interval orders). These combinatorial results are used in another paper to develop a stochastic theory describing the emergence and the evolution of preference relations (Falmagne and Doignon,[7]).

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