Well-graded spaces of valued sets

Authors:
Sergei Ovchinnikov
Affiliations:
Mathematics Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA
Venue:
Discrete Mathematics
Year:
2002

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Abstract

Well-graded spaces of valued sets and relations are introduced and their properties are investigated. In particular, it is shown that the space of valued partial orders on a finite set is well-graded. This is a generalization of a well-known result of Bogart (J. Math. Soc. 3 (1973) 49). Motivation for these studies comes from media theory (Falmagne, J. Math. Psych. 41 (2) (1997) 129; Discrete Appl. Math., submitted) where well-graded families of usual sets play an important role.